Yes it’s true… because you’re literally scraping the tape across the play/record head in the deck as you dub. Every time you do this the tape can become SLIGHTLY more degraded and fragile. That said, there’s not much difference between recording over a previously recorded tape and scrubbing back and forth with the jog wheel over a house master for 10 minutes (in fact, the jogging is probably worse, but you rarely hear anyone talk about how that’s terrible for the deck).
The real issue is the tape, not the deck. It’s best to record new material over clean tape to ensure that you’re recording the best possible signal. If the tape is new/clean, you’re less likely to encounter an area on the tape where there is a glitch, or where residual metal flakes on the heads may have collected on the tape (over the course of a previous dub session, perhaps), thus causing recording errors. Clearly, performing insert edits on tapes works fine and is acceptable, but nonethelss… in practice it’s best to make dubs on clean tape.
-Ben