They told you you "really should have phoned in" who? You can't call the restaurant to find out if they participate, because often no one there except the owner knows! That's the whole point of this program, it's supposed to keep who gets the earnings secret from the staff serving you, etc.

So did they tell you you're supposed to call Rewards Network customer service prior to every dine to verify that their website is correct???

Or did they claim some automated phone service of theirs is more accurate than the website? (Bah humbug, I bet if you'd used an automated phone service of theirs, you would have had just as much of a chance of the same error, except unless you recorded it you wouldn't have any proof in that case!)

This sounds like you were given a bogus answer, and you should have called back and spoken to someone else (or asked to be kicked up to a supervisor). They should have accepted a printout from the previous day fased to them as proof that you should have goten the miles, and I'm pretty sure other people have documented that happening in other threads here in the past.