Before posting this, I thought I'd try to find an example of the kind of skeptical comment I heard previously. The following is close:
There occurs not a shred of evidence for a city named Nazareth at the time of the alleged Jesus. [Leedom; Gauvin] Nazareth does not appear in the Old Testament, nor does it appear in the volumes of Josephus's writings (even though he provides a detailed list of the cities of Galilee). Oddly, none of the New Testament epistle writers ever mentions Nazareth or a Jesus of Nazareth even though most of the epistles got written before the gospels. In fact no one mentions Nazareth until the Gospels, where the first one didn't come into existence until about 40 years after the hypothetical death of Jesus. Apologists attempt to dismiss this by claiming that Nazareth existed as an insignificant and easily missed village (how would they know?), thus no one recorded it. However, whenever the Gospels speak of Nazareth, they always refer to it as a city, never a village, and a historian of that period would surely have noticed a city. (Note the New Testament uses the terms village, town, and city.) Nor can apologists fall on archeological evidence of preexisting artifacts for the simple reason that many cities get built on ancient sites. If a city named Nazareth existed during the 1st century, then we need at least one contemporary piece of evidence for the name, otherwise we cannot refer to it as historical.(source)
Now, I'm not sure if they'll find any specific usages of the word "Nazareth" on the house, but that's not an especially reasonable request, so we'll leave the evidence where it stands.