Got this reply from HostMySite.com's support tonight:
"Unfortunately due to resource and security issue, we do not support the installation of Drupal on a shared account."
Surprising, since i have 10-12 domains hosted there on shared, several of them using Drupal, and i've been advising clients to use HMS for years. I've had my ups and downs with HMS for probably 5-6 years, but I've tried (and continue to try) others from time to time and no one has yet touched HMS's 24/7 human phone support.
The support ticket, which by the way requested more PHP memory, mod rewrite enabled, and looking into why FTP wasn't working, was a similar one I call about every time i setup a new account that will have Drupal. More memory, and mod rewrite (the FTP thing was an oddball issue). Until tonight they've always cheerfully, quickly set it up.
So i called support. The tech i got said something didn't sound right to him, that HMS sets up Drupal all the time. However when he checked with a supervisor he said he was just informed it was a new policy. No Drupal support on shared. I explained i didn't want Drupal support. I wanted mod rewrite enabled and all the PHP memory they would bump to. So he checked with manager again. This time, he said, they'd go ahead with the requests. But he said i needed to look into VPS.