Actually he would know as well as anyone that coming in at 10 AM with relatively few there, inconspicuous on a bike including a helmet that hid his identity would make that very, very easy.
I have seen numerous pictures of Arnold on a bike, and have never seen him wear a helmet. At most - sunglasses. As iconic and recognizable Arnold is, I just find it hard to believe that "nobody noticed".
Now, if he DID in fact wear a bicyle helmet and sunglasses, then yeah, maybe I'll buy that nobody noticed.