Do standalone Oblivious Transfer (OT) Protocols exist? Are there any Oblivious Transfer (OT) protocols that don’t rely on asymmetrical encryption, public-key encryption or key-exchange?

I’m starting to wonder, as all the OT protocols I know of (and can understand how it works), rely on such an encryption layer. Are there any out there which is somewhat-standalone and does not depend on the security of the scheme/protocol it uses underneath?
The term "stand alone" in secure computation typically refers to the case of a protocol being run once, and not to assumptions. In any case, what I assume you are really asking is what assumptions are needed for OT. You are indeed correct that OT is built from asymmetric assumptions, and this is actually inherent for black-box constructions. This was studied in The Relationship Between Public Key Encryption and Oblivious Transfer.