I don't believe Snap Manager for Oracle requires ASM.
The problem used to be that asmlib wasn't supported, and didn't function, on RHEL 6. Snap Manager for Oracle has to have asmlib to work, if you use ASM.
Looking at the support matrix, Redhat 6.4, SnapManager 3.3, FC, and Oracle 11.2.0.3 are compatible.
That said, you want to be 100% certain your intended configuration is supported and tested before you start. Getting this all to function for us wasn't what I'd call easy.