edam, don't be worried about my post!
It's true though that most babies are put to sleep on their tummies in the USA.
And it's also true that there are many ways of doing things, and I feel in this instance - new mummy with a new baby and OP already has a reputation - undeserved or not - as a know it all that I wouldn't interfere TBH.
I read this in a scientific journal: Apparently it's the moving a baby from one way to another that causes most problems and deaths. If she's used to going asleep on her tummy she should stay going asleep that way.
I stand by this - we all have our opinions about everything but not worth alienating a new SIL about really. I would say nothing.
I still feel that I am sorry about the OP's brother, and hope she isn't feeling too stressed about this. I think the OP may be hypervigilant about her brother, and might bebefit from talking it over with someone rather than alienating a new mum (her SIL) with her own fears TBH.
If I had to do something I would ask my DP to have a word with his brother, but not to say anything to his DP herself. I still stand by this advice - it's easy to get too involved with an outcome you desire, rather than looking for the best for everyone.
Many people put their baby to sleep on their tummies - I have read research that suggests it's the moving from one way of sleeping to another at the 3 month stage that causes problems, and as mii posts that there were a lot of other advices given at the time of the Back to Sleep campaigh which also atlered the statistics.
So I would still do nothing, maybe have a word with my Dp's brother. I would have a chat about my DB with someone if I was the OP though.