The tapes may
be stable (I'm suspicious of that claim: their temperature tolerances aren't as high as modern hard drives, they actually care about dust, and I would expect them to be more susceptible to magnetic interference); but the tape drives
are not. Over time drive heads become misaligned. They continue to write fine and can read what they write; but sufficient misalignment prevents other
drives of the same type from reading the tape. That tape then becomes only as useful as the drive that wrote it. Lose the drive, you lose the use of the data on the tape. Unless you test reading the tape in a different drive than it was written from (while the writing drive is still available for pulling the data out), this condition's effectively undetectable until you actually need the data.
There's a reason so many shops have moved to disk based backups. Tape simply isn't reliable. Tape is cheap; but definitely NOT reliable.