> Uh, and that fix? I don't even see a file named Product.php - looked at the original download package for 2.0.1. Wut?

The fix is for 2.1.0. I can't repro anything like the issue you are reporting in 2.0.1.

Possible root cause: you should not have a copy of admin/includes/modules/product/collect_info.php - did you copy an old customized one in there?
Or are you using a different product type than "1"?