Found the cause of the problem – and fixed it!
It turns out that LF vs. CRLF is not an issue at all on a LAMP based webhost.
The problem in my particular case was that I copied the original theme’s style.css verbatim, and it was missing a very critical line in the comment section:
Template: twentyeleven
Once I fixed that everything started working as expected.
Note: Template should point at the parent’s directory, not the child’s one.