This should really be a comment, as I have only partial information and am neither able to conclusively strengthen or refute the claim, however I can throw some information into the debate.
I'll start with the part of the claim that "specifies" what happens:
eventually needs glasses
Besides the (trivial) fact that almost everyone eventually needs glasses I think that glasses help only in very special cases of welding-related eye damage:
AFAIK types of eye damage are typical for welding are (eye damage info by the Institute for Occupational Safety and Health of the German Social Accident Insurance):
a) arc eye (photo-keratitis) is a damage of the cornea that is usually reversible (though very painful) and heals within a few days.
Possible link to glasses: I could imagine that scarring can occur with bad burns (as it can happen with other "normal" burns of the cornea). Scars of the cornea can lead to a wrong curvature which may be corrected by glasses.
b) cataracts: long-term exposure of the eyes to UV can lead to cataracts, this damage is irreversible.
Here's a link to glasses: cataracts surgery removes the lens of the eye. Nowadays in industrialized countries, the lens is replaced by a plastic lens. Before these were available, people had to use very thick glasses after the surgery.
c) VIS light can lead to retinal damage (thermal or photo damage), which is also irreversible.
Glasses don't help against this.
Now for the main claim:
auto-darkening welding helmets are dangerous
The possible mechanisms of danger compared to conventional masks can be
not all dangerous radiation is filtered (see below)
the automatic masks have a reaction time of 0,1 ms claims 3M on p. 38, and during this time dangerous radiation may flash the eye. For coparison: this is about 1000 times faster than the Corneal reflex[which however is too slow for eye protection against the arc].
However, if I read their table correctly, that applies to the VIS part, the UV filter is permanent of class 13.
A pubmed search did not turn up useful material.
However, I found out that in the EU, EN379 regulates automatic welding filters (behind paywall, I don't have access).
Two things that are for sure dangerous with the automatic filters are:
Personal experience (no long time experience with automatic mask but with a conventional helmet, and only hobby welding, though):
it is far easer to flash your eyes with a conventional mask, either by accidentally looking through a low filter class area, or by nodding a bit too late/accidentally starting the arc on the wrong place/too early.
I was particularly interested to find any working safety studies on this aspect, but I didn't find anything, so for now this remains anecdotal.
I have far more "events" of getting flashed by someone else welding than by my own, but the latter is of course more dangerous because of the closer distance.