Wrong Windows binaries/lib files?

I’m wondering if the files in the Windows x86 and i686 distributions have been mixed up.
I’m running Windows 7 on an Intel Core i7 processor, and for some reason my hello world program compiles only with the i686 lib files, but will run only if I provide the x86 dll’s.
Something must be wrong with these distributions…

Forgot to mention (and I can’t edit my post!) that I’m referring to the SDL2-devel-2.0.0-mingw distribution.

Also, I noticed this weird fact:
in SDL2-2.0.0-win32-x64.zip and SDL2-2.0.0-win32-x86.zip, the SDL2.dll files are reversed, compared to those in SDL2-devel-2.0.0-mingw.tar.gz.
Something is messed up for sure.