It's been a while since I last set up Hylafax, and I don't actually remember the details. But most of the problems I recall were indeed due to limited file access rights for a user or a program.
One thing I recall is that for recent Hylafax versions it is best to set up Class 1, regardless what the faxmodem supports. Class 2 and Class 2.0 support more functions in hardware, which is good for maximum performance. But the implementation is often flawed. The effect was quite similar to what you describe, so it might well be a problem caused by your faxmodem. Class 1 leaves maximum control to Hylafax. Usually this works very reliably.
But I suggest that you post your question at the Hylafax users mailing list. The folks there have solved *all* my problems with Hylafax in the past, and they did so quickly.