Are prime brokers allowed to copy your trading strategy? Or do you sign a contract saying they wont?
Being a good prime broker is also a lot of work, and is an elaborate and involved process.
Now for the firm to take on two jobs, and then keep it secret... I wouldn't worry about it. It's like worrying your accountant is going to take your successful startup idea and run with it because they know how much money you make.
And in all markets, that's one reason why many firms invest in transaction cost and best execution analysis, to make sure they're not getting front-run when they see abnormal dips in broker quality.