People who own expensive cameras tend to use one and ONLY one type of tape period. People who own cheaper cameras tend to throw in any kind of tape- used or new. The only danger is gunking up the heads which I suppose could in turn ruin a tape. That said I can't imagine that a well maintained cheap camera could ruin a tape.
I've only once had a tape get ruined, and it caused by an expensive Sony DVCPro/MiniDV deck. The deck ate it just like car stereos used to do before the days of CD. In know this is hardly conclusive, but my impression is that even cheap cameras are amazingly reliable considering the complexity and delicacy of the mechanisms. They do start to fail over time, but this doesn't generally put tapes at risk, it just prevents proper playback or recording (whether mixing brands presents a problem is unclear)*. However, I would remcomend not reusing tapes, and suggest using pro-grade tapes where the tape will spend a lot of time in a camera/deck being during post as they are relatively sensitive compared to, say, Beta SP.
*I have an 8-year-old VX1000 that I've used every type of tape know to man in--and was once dropped with on the tapeloading side with the door open--that to this day has never needed a cleaning, let alone experienced any recording or playback problems.
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