Yes, you can have x86 installed on a 64 bit machine.
Microsoft said that because their 64-bit version of Windows wasn't stable. For programs that use lower system calls, making it work with 64 bits is more complicated than just recompiling it. They have to actually change a lot of the code and figure out work arounds, which is why it wasn't stable. The linux x86_64 kernel is stable, but there are still some issues with applications that work well in 32 bit but haven't been transferred over to x86_64.
However, if you have x86 installed on your amd64, then you should just consider it an x86 system (with the capability of becoming an x86_64 system).