It’s plausible Orochi played a trick for Oden to be beaten, but I don’t think that’s how he betrayed him.
For starters, it would undermine the effort the Strawhats and allies go through trying to beat Kaido and the lead up to him if Oden could just 1v1 him. And I take a lot of Oden’s current hype to just build up to how monstrous Kaido is.
Secondly, I think what Orochi did to Oden was more personal. Betraying Oden to help Kaido betrays him and Wano, but the way Kin’emon recounted the events, and how everyone reacted, it seemed more of a betrayal directed at Oden specifically.