Not in the park based on the fact that one does not need a Quetico camping permit to be there - only a crown land camping permit.  Anyone can drive to the BH parking lot (one reason for the lot expansion) launch a canoe and camp on the lake without ENTERING the park.  So, it's out.  Ditto with French lake although my maps show a fuzzy red line around that lake too.

So, to recap....
Do you need a Quetico Camping permit to camp in Quetico Park?  Yes.
Do you need a Quetico Camping permit to camp on BH?  No
Logic, and the real Park Boundaries here as demonstrated by park rules and by definition will demonstrate that BH, as a whole, is not a Quetico Lake.  I say "as a whole" because of changing high water levels.  Like when the BH Ranger station was underwater one year.  Then I suppose BH was encroaching over the park boundary.

I'll stop in when I'm down that way Wally.  We can go to the store together where I can pick out a bottle.   ;D