I paddled through there in mid-July with my daughter. We were thinking that we could easily reach Nels lake (outside of the bwca) and camp there. There is one campsite on Picket lake, it's in the northwest corner as you head out of the lake (away from the Mudro put-in). We didn't stop there but it looked like it had a flat granite outcropping and the landing looked shallow.
I can't say more about it but the Kawishiwi Ranger station has a hand-out (might be up on their
website ) for dispersed camping sites.
As an FYI, we didn't make it to Nels. We found the first bushwhacking portage around a muddy beaver dam area and continued across the lake/marsh to the stream that leads to Nels but we ran out of water before we found a trace of the portage that supposedly is located on the north shore of that stream.