Of course. I actually regard this as a fairly major issue with the Linux permissions model. Far too many people do as the GP and accidentally set all the files to executable. Cleaning up after someone has done this on a nested set of subdirectories is quite tedious.

NB if anyone has ever run: chmod -R u+x . or equivalent and you run chmod -R u=rwX the files will stay executable...

You can always use find to set all files to +x and directories to -x but then what if some of files needed to be executable?