You are correct in that the stench pipe allows air in behind the water which allows for better drainage, but the problem could be due to incorrect fall of the soil pipe, roots etc building up inside the pipe or even not enough water being supplied from the flush due to a low cistern level or water conserving brick inside....a plumbers worst nightmare is the use of really thick loo paper (charmin springs to mind), sanitary towels and tampons being flushed down or worse still, the disposable nappy.....only put down the loo what you've eaten first is the golden rule!
John
June 2009