How is it I could discern the actual hearders sent by the server? Could I use wget somehow for that purpose?

Try this:
man wget

and then this:
wget -S -O output.html http://domain.com/file.html

Try manually creating a file in the same directory as the html file. Try foo.txt and foo.html. Check the permissions on the directory itself (and all parent directories) they should be 755.

Since the question is really Apache related try http://www.webmasterworld.com/forum92/.