I think if the grill closes at 10, then yes, it should be posted. Because if I was going into a counter service restaurant that claimed to be open 24 hours a day, I'd expect to be able to order off the menu. I mean, that's just smart business, in my opinion.
And on another note, I think some people (and by NO means, ALL) that have the opposite opinion are being extremely rude and hard on the OP. It's fine to have another opinion, but it's another thing entirely to talk to someone in a condescending manner simply because you don't agree with them.