Mr. Bellisario quotes from an Archbishop discussing the tower and dove arrangement that existed in a few ancient churches.
What Mr. Bellisario overlooks is that the tower and dove are not the tabernacle. They had a similar function, to hold the elements, but they do not represent the tabernacle of modern Catholicism.
In fact, according to Maurice Hassett, "Our present form of tabernacle dates from the end of the sixteenth century." And the very Archbishop from whom MB quotes admits, "One must wait for the 16th century to find the tabernacle fixed on the greater altar and, later still, to see it placed in the middle of the table, the last phase of historical development of the altar." (loose translation of the Italian original)
Furthermore, one can see the development of the tabernacle in the Archbishop's own paper. As the Archbishop noted, during the Gothic period there were a couple of places that the bread could be found. The tower and dove (which were suspended above the altar) might be veiled, but the consecrated host could be found in the armarium more conveniently at hand.
Sometimes you reposed custody under the altar, as indicated by the Statutes Synod of Liege, 1287: "Corpus Domini in honesto loco, sub altari vel in armariolo sub clave custodiant." Usually, however, custody is kept in a cabinet or kiosk, dug into the wall, right or left of the altar.
The Archbishop goes on to explain how these armaria came to have doors with elegant fittings and paintings (particularly in the more glorious churches). The door was provided with essentially a window that allowed the faithful to worship the transubstantiated sacrament from outside, and a lamp was provided in front of the window to show where the sacrament was kept.
Over time, these armaria developed from a simple closet to more elaborate designs. Thus, the Archbishop reports that in the 14th century there emerged "edicole del Sacramento," which seem to eventually have served as the predecessors for the modern tabernacles (though, at first, these edicoles were found exclusively in northern Europe).
The Catholic Encyclopedia (which Bellisario thinks to be such an insignificant source) mentions, "The Fourth Lateran Council and many provincial and diocesan synods held in the Middle Ages require only that the Host be kept in a secure, well-fastened receptacle. At the most they demand that it be put in a clean, conspicuous place. Only a few synods designate the spot more closely, as the Synods of Cologne (1281) and of Münster (1279) which commanded that it was to be kept above the altar and protected by locking with a key."
But, of course, one need not rely on Catholic encyclopedias alone:
Steven Schloeder, in his book, "Architecture in Communion," writes that "Toward the end of the twelfth century the tabernacle began to be used and slowly gained prominence until it was universally legislated in the nineteenth century." (p. 96)
William Thomas Cavanaugh, in his book, "The Reservation of the Blessed Sacrament," writes that "As was said before, the use of the tabernacle began to spread rapidly on the promulgation of the following decree of Pope Innocent III in the Fourth Lateran Council." (p. 61) The Fourth Lateran Council is normally dated to 1215.
Gerald Ellard likewise writes, in Christian Life and Worship, "The Tabernacle Introduced. Nothing has been said in the foregoing paragraphs about what is now regarded as the central feature of the altar, the tabernacle. The altars then had no tabernacles. The whole realm of non-sacrificial worship of the Eucharist was beginning to manifest itself only in the eleventh and twelfth centuries. Moreover, even after this type of devotion developed and was spread rapidly (as a consequence of the establishment of the feast and public procession of Corpus Christi in the thirteenth century), there was still no need of a tabernacle at the altar, because the new devotion was non-sacrificial." (pp. 115-16, emphases in original) (it's worth noting that Ellard views the suspended doves as a form of tabernacle)
So, in conclusion, Dr. White is vindicated against Mr. Bellisario's criticisms. While consecrated bread and wine were stored prior to the introduction of the tabernacle into Catholicism, the tabernacle was a development, as attested by Mauro Archbishop Piacenza, the very Archbishop that Mr. Bellisario relies on in his video. Here is a link to an English version of the essay (UPDATE: here is a link to an English version of Piacenza's article).
Mr. Bellisario's category error is in confusing the genus of casings of the Eucharist with the species of the tabernacle (a particular kind of casing that did not arise until after the innovation of the doctrine of transubstantiation). Unlike the veiled tower and dove (through which, it seems, the consecrated bread and wine would not be visible) the tabernacle provided a display of the bread and wine so that these elements could be worshiped (while still securely locked up). I hope this post will serve to encourage him to rethink his video (link to video) and particularly to apply more thoroughly the principle he lays out at the beginning, namely "I try to be charitable when I do these things ...."
Finally, for the reader's convenience, I have embedded below the video to which Mr. Bellisario was responding:
UPDATE: Prior to publishing this, I happened to stop by Mr. Bellisario's blog and noted that he has republished an article by Francis J. Schaefer, which confirms the same thing: (link to MB's republication). As that article states:
As a permanent substitute for all of these receptacles we have the tabernacle, as we see it today; i. e. the small case or cabinet of rectangular or of round shape, placed right above the center of the altar. The name of tabernacle given to it, as well as the object designated by the name, has come into general use in comparatively recent times. The word tabernacle has been used since the middle ages; but its occurrence is not very frequent. It is found in the Constitutiones Synodicae of Odo, Bishop of Paris in the twelfth century; in the Rationale Divinorum Officiorum of William Durandus, a learned canonist of the thirteenth century; and in a decree of a council held in the city of Alix, southern France, in 1585, where detailed regulations are laid down for the construction and maintainance of the tabernacle. The Council of Trent (1545-1563) decreed that the Blessed Sacrament be reserved in the churches (Sess. XIII., Cap. VI., Can. VII.); but in designating the receptacle for it, it has recourse not to the word tabernacle, but to the word Sacrarium. Since then, however, the word tabernacle has been used regularly in ecclesiastical legislation, e.g. in the decrees of the Sacred Congregation of Bishops and Regulars, 29 November, 1574) and 10 February, 1579, and also in the decrees of the Sacred Congregation of Rites, 21 August, 1863, and 6 February, 1875. The liturgical books, such as the Caeremoniale Episcoporum and the Roman Ritual, which give directions regarding reservation of the Blessed Sacrament, also make use of this expression. (emphasis added)(alternate source)