A direct owner rental transaction requires a degree of faith not only from the renter but the owner, too. Just as you don't know the owner she doesn't know you. I suspect that's the genesis of her hesitancy to give out her telephone number (unless the email conversion went just the way that you described; if you asked her to call you then it only makes sense that's she'd ask for your telephone number and not offer her's). While it's pretty likely that there's nothing wrong with the potential rental, it sounds like both you and the owner want to be in control of the transaction and, maybe, both of you are a bit suspicious of the other. If that's the case then I wouldn't blame either of you for just walking away from a transaction with which you're uncomfortable.
On the other hand, I've rented timeshare weeks from owners - none of whom I've ever met - five or six times in a variety of locations (all before redweek.com was created) and I've never had a problem. I think that I spoke directly with an owner just once. If I recall correctly most of those transactions were initiated through
www.tug2.net and one was through ebay. But if I hadn't subsequently purchased a couple of timeshare weeks I'd have no particular concerns about using redweek.
Just my two cents.
Dick Taylor