As his first commenter notes, however, the passage he quotes is a bit outdated, because it refers to indulgences that remit "time" in Purgatory. Now that Catholicism is changing to stop talking about "time" in Purgatory, these old indulgences do not make sense. Only the "plenary" indulgences make sense, and so those are the only ones left. (Update: there is still the concept of a "partial" indulgence - but now that time has been eliminated, it is somewhat difficult quantify parts in a way that would permit the indulgence to be coordinate with the act performed. Thus, as a practical matter, the plenary indulgences would be expected to - and do - dominate the indulgence scene.)
This provides a great example of one of the many changes in Catholic theology that took place in Vatican II. Oh - we know the counterargument: the idea that there is time in Purgatory had never been dogmatically defined, and consequently this isn't a change.
But think about it. If all the popes and other Catholic teachers promulgated (and - in previous generations - sold) indulgences that were absolutely meaningless (if, in fact, there is no "time" in Purgatory) then what's the explanation?
1) The "Church" didn't know the truth about Purgatory; or
2) Something else?
Or perhaps someone will come back with a new counter-argument that the post-Vatican II position also hasn't been dogmatically defined, and just because there are no more time-based indulgences doesn't mean that there is no time in Purgatory. On the other hand, the CCC now states that "death is the end of earthly time" (I don't recall the citation offhand), and the CCC nowhere suggest that there is time in purgatory (to my knowledge).
On top of that we have, in Spe Salvi, essentially a promulgation of a denial that Purgatory is a place where time applies:
Who would not feel the need to convey to their departed loved ones a sign of kindness, a gesture of gratitude or even a request for pardon? Now a further question arises: if “Purgatory” is simply purification through fire in the encounter with the Lord, Judge and Saviour, how can a third person intervene, even if he or she is particularly close to the other? When we ask such a question, we should recall that no man is an island, entire of itself. Our lives are involved with one another, through innumerable interactions they are linked together. No one lives alone. No one sins alone. No one is saved alone. The lives of others continually spill over into mine: in what I think, say, do and achieve. And conversely, my life spills over into that of others: for better and for worse. So my prayer for another is not something extraneous to that person, something external, not even after death. In the interconnectedness of Being, my gratitude to the other—my prayer for him—can play a small part in his purification. And for that there is no need to convert earthly time into God's time: in the communion of souls simple terrestrial time is superseded. It is never too late to touch the heart of another, nor is it ever in vain.
(take from paragraph 48 thereof, emphases added, source)
Thus, I think it's safe to conclude that this is an example of Catholicism teaching "X" 50 years ago (i.e. before V2) and "notX" now. That's usually the standard that we're asked to provide by Catholics who want a demonstration of the fact that the Roman Catholic church makes mistakes, and consequently cannot be trusted in the same way we trust Scripture.
In short, Dr. White's point is emphasized by this very matter. If Catholics simply accept what Rome teaches, they are going to be accepting error as truth, because the Roman Catholic church makes mistakes.
UPDATE: "The Hidden One" has disputed several "factual matters." He doesn't specifically come out and say that it was not previously taught that there was time in Purgatory. It's good he didn't because, as Thomas Aquinas wrote in Summa Theologica, "the punishment of purgatory is temporal" (See reply to Objection 4, here) and "The fire of Purgatory is eternal in its substance, but temporary in its cleansing effect" (See reply to Objection 1, here) and "a man may be punished at the same time for sins committed in various places" (See main answer, here) and "And since that which clings more persistently is more slowly cleansed, it follows that some are tormented in Purgatory longer than others, for as much as their affections were steeped in venial sins." (See main answer, here) and "Severity of punishment corresponds properly speaking to the amount of guilt: whereas the length corresponds to the firmness with which sin has taken root in its subject. Hence it may happen that one may be delayed longer who is tormented less, and "vice versa."" (See reply to Objection 1, here)
Furthermore, it is not only a medieval belief, but one that was reflected in the modern era (before V2). For example, see the comparison of three days in purgatory versus three years of suffering on Earth in this aid to understanding the Baltimore catechism (link). See also the discussion in the right hand column, about mid-way down (with various citations) here.
Erasmus points out the belief that there is time and days in Purgatory according to the prevailing belief in his day (link). (See also, footnote 3, here - especially the portion on the following page).
There's a very lengthy discussion here, if anyone is interested.
Likewise, numerous non-Catholics have recorded the same thing (see here for example, especially pp. 375-77).
In fact, we could go and on.
James Akin's undocumented claim(s), "The number of days which used to be attached to indulgences were references to the period of penance one might undergo during life on earth." (here) and "This document introduced the classification of indulgences as partial or plenary—a simplification of an earlier system of reckoning how many "days" of penance an indulgence represented that led some to suppose that an indulgence represented getting a certain number of days "off" their time in purgatory." (here, emphasis in original - same website as previous quotation, but attribution to a particular author is unclear) do not persuade me to the contrary, since Aquinas and many many others are clear that Purgatory was temporal and temporary. Indeed, Aquinas believed that Purgatory was a place (not merely a "state") and that it was either in or near hell. He also held that the fire of Purgatory was real physical fire (and the same fire as Hellfire), which would require time in order to burn, since burning is an action.