This is correct from the perspective of direct health hazards, but there are still plausible risks. We know from history you don't need a lot of mass to cause global problems, if the material is catalytic.
If the vaporized satellites were entirely converted into a compound that was as damaging to the ozone layer as the most potent CFC (R-12 [1]), and the compound stayed in the atmosphere forever, it would take 5,000 years to reach current atmospheric concentrations of R-12.[2]
Vaporized satellites really don't seem like a concern.
The first is that IIUC, CFCs release chlorine atoms which catalyze ozone, whereas aluminium oxide catalyzes the creation of chlorine atoms from chlorine reservoirs, which then go on to catalyze ozone. I loosely believe at this point after some sketchy research and maths that this makes it around two orders of magnitude more potent.
The second is that these particles are produced directly in the upper atmosphere. I couldn't give you a number for how much that changes things, but I assume it's nontrivial.
The final point I've noticed is that mass to orbit has been increasing at a rapid exponential rate recently, and it would not surprise me at all to soon see an extra order of magnitude on it.
Worst-case, that could change your 5,000 year figure to just a couple. I don't think it's that bad, I'm not overly concerned about this issue, but given ozone depletion is a legitimate existential threat and the numbers don't immediately make it seem impossible, I think it's worth paying attention to.
