Does anyone know of a comparison, benchmark or similar which proves there's no significant performance hit to using foreign keys ? (Which I hope will convince him)
I think you're going about this the wrong way. Benchmarks never convince anyone.
What you should do, is first uncover the problems that result from not using foreign key constraints. Try to quantify how much work it costs to "clean out invalid references". In addition, try and gauge how many errors result in the business process because of these errors. If you can attach a dollar amount to that - even better.
Now for a benchmark - you should try and get insight into your workload, identify which type of operations are done most often. Then set up a testing environment, and replay those operations with foreign keys in place. Then compare.
Personally I would not claim right away without knowledge of the applications that are running on the database that foreign keys don't cost performance. Especially if you have cascading deletes and/or updates in combination with composite natural primary keys, then I personally would have some fear of performance issues, especially timed-out or deadlocked transactions due to side-effects of cascading operations.
But no-one can tell you- you have to test yourself, with your data, your workload, your number of concurrent users, your hardware, your applications.