This is exactly how I interpret it.
The identities and personalities of everyone involved and the events that transpire are canon. Exaggerated facial expressions, body contortions, unbelievably survivable flights/falls/impacts, credits, curtain calls, and other comedic shenanigans are comedic shenanigans added to the story by whoever has chronicled our adventures, to entertain posterity.
Canonically, the WoL is smart enough to know when a Primal can't be reasoned with and when to have friends on call for backup. Journal entries as far back as ARR indicate that not all Primal fights are 1v1:
(Alphabetized to obfuscate story order)
(Not a complete list)
Bismarck:
Lakshmi:
Shinryu:
Shiva:
Susano: