Sure, but one of the Codes highlights how heat can damage stones. (And lichen?) and might cause further damage. Some people might have the sense to leave a big enough gap but you know how barbeques throw out a lot more heat than you expect and I don't think good sense is equally distributed.
OK, it's me, I'm crabby and nitpicking but if some use braziers others won't bother (what a chore to bring one) and some who aren't even spiritual types will think any fire is OK - and there's evidence of that in loads of places.
Told you I was crabby. To me, lighting a fire inside a stone circle shows less evidence of spirituality than of complete prattishness.
Theory: not EVERYTHING that is claimed as a spiritual right should prevail. It ain't an infallible trump card.
;.#