No, though HMACs can play a role. It was a protocol developed specifically for establishment of secure, encrypted, authenticated, and integrity-protected sessions.
I've been racking my brain trying to remember (rarely accessed memories from ~27 years ago). The basic challenge is that unless authenticity, key exchange, and integrity are managed simultaneously during session establishment, there are attacks possible against whatever was omitted. There was a protocol developed at that time that did all of the above as part of session establishment, but I don't remember it really taking off (IIRC, it was patent-encumbered, and that was an obstacle to adoption).
I've been racking my brain trying to remember (rarely accessed memories from ~27 years ago). The basic challenge is that unless authenticity, key exchange, and integrity are managed simultaneously during session establishment, there are attacks possible against whatever was omitted. There was a protocol developed at that time that did all of the above as part of session establishment, but I don't remember it really taking off (IIRC, it was patent-encumbered, and that was an obstacle to adoption).