Not really. You can combine the public random source with a secret key. Since you assume they can keep secret a random source, they can equally keep this key s

Not really. You can combine the public random source with a secret key. Since you assume they can keep secret a random source, they can equally keep this key secret. In fact, it's sometimes preferable to get rid of hardware source completely and only rely on a secret key and a state, and obtain a design that is more resistant to fault.