I got parking comped on a free night at the Grand Hyatt a week or two ago. Remember that it's not about whether the parking is "run" by the hotel but whether it is "billed" to the hotel, and the $52 valet parking charge is absolutely billed to your room at the GH DC.

By the way, I don't think your $529 rate was a mistake, it is frequently that high (although also frequently <$200). I have stayed at this property a few times. It is not worth the >$200 price tag, but it is a perfectly pleasant place to stay with a location that is hard to beat. The Grand Club is also fairly decent in the evening -- a good selection of liquors are available for $4 a pour.