I had Veeam support remoting into my environment twice, with no results.
The suggested registry change brought no improvements.
After asking the same questions more times and receiving several logs from my side, their final word was that "the tapes were written with a product that made them unreadable by Veeam" or something similar.
Which I find rather strange, given that
a. the product in question was IBM Tivoli Storage Manager, quite widespread I believe, and
b. the mt.exe application was always able to "fix" each tape instantly (I don't even think it really makes access to the tape, since it takes literally no time to return the prompt).
I have no more tapes showing the problem as I've had to "fix" them with mt.exe and use all of them for the backups. I waited for more than two weeks before using the last ones, in order to leave support time to investigate, but apparently to no avail.
The case is now closed with no results, and with no satisfaction from my side. Sure, I could always use mt.exe, but this is just a workaround as somebody said, not a solution.
First time I am disappointed by the Veeam support.