So they'd terminate purely based on their own 'suspicion'? Seems a little harsh.
Acting on anything short of proof, is acting on suspicion. Now what constitutes proof as far as copyright infringement? I can't think of anything short of a court decision. DMCA takedown notices aren't proof, they're just when the complainant swears they have a good faith belief that the file in question is infringing.
An external request to take something down is different to making that decision entirely on your own suspicions.
Typically, this is covered by the "we can do whatever we want"-type clause in other file providers TOS, bayfiles is just limiting their purview to more specific situations.
My point with my previous point was that any harshness was not on the part of bayfiles.