Russ,
this absolutely should not be the case.
Your client version (32/64 bits) is not relevant when it comes to connect to DB from sqlplus.
Basic rule as it was mentioned above is 32 bit app needs 32 bit client to connect to DB.
I use Win 64 bit, have both 32 and 64 bit clients.
Both can access any version of DB (and believe me I work with quite a few of those).
Keep in mind you have to configure your tnsnames separately for 32 and 64 bits.