it seems risky for them to shop a product they ultimately might not hold rights to if a deal comes to the table
Most "Shopping Agreements" would have a clause in it stating that the producer would be protected if the company he brought it into decided to do it at a later time.
Lets JoeBlow Producer has a "shopping agreement" with a writer for a script called "Dead Rider." JoeBlow producer brings the script to Silver Pictures, Joel Silver decides to pass. Then a year or two down the road another producer, Number Two Films brings the "Dead Rider" script into Silver Pictures, of course after extensive rewrites, and Joel Silver decides to do it... Then JoeBlow Producer gets wind of the deal and lets everyone know he brought the project in a year earlier. He would automatically be attached.
I've seen it happen on a big film that just lately came out, with a producer I know.