My understanding is you need an Ontario fishing license to fish in Ontario and a Quetico permit to be Quetico. If you want to get out of the canoe and step on Crown land (other than a portage) you will need a RABC permit.
My guess is the most likely official you’d encounter would be a Quetico Park ranger that would ask to see your Quetico permit.
When I do my Spring BWCA trips and my route will take me on Border Lakes within Quetico (eg Crooked) I carry the following three items with me:
Seasonal day use permit RABC permit Ontario fishing license Per the season day use vehicle permit, it’s one per canoe.
I have found Quetico Park Superintendent Trevor Gibb to be pretty responsive to my questions. His email is: Trevor.Gibb@ontario.ca
For additional info see
this thread and search other posts on this site.