Your equation for the gamma factor is correct. You are also correct in saying that they Lorentz transformation becomes undefined. The significance of this is that it makes no sense to talk about the "frame of reference of photon". Lorentz transformation equations allow us to switch from some set of time and space coordinates to another one moving at speed V < c relative to the first one. They make no sense for V = c or V > c.

I think that what Tyson meant by his somewhat imprecise answer was what I said in my comment above: if you take the equation t *gamma = T (that relates the time t that passes between two events for an object that moves with V from one to the other, with the time T that passes between between the events on a rest frame) and take the limit V approaching c for finite T, you get t = 0. If you want to keep the meaning of the equation in this limit, you have then to say that "no time passes for a photon". The issue is that the equation is just a consequence of the Lorentz transformations, which are inapplicable for V = c, and as a consequence the words "no time passes for a photon" do not have any clear, operational meaning attached to them.