Well, I agree that the altimeter would be set at 28.62. There isn't anything in the AIM that says it isn't recommended to fly with a pressure that high. It does say that flight isn't recommended when pressure is lower than 28.00. The FARs regulate the height of the lowest flight level, which in this case would be around FL195. At first I was thinking that that's what you were getting at, but certainly that wouldn't ground you.
The only other thing is that the temperature is lower than standard for the altitude, something like 37*F, which would make your altimeter read lower than normal.