I saw the formula in Abu-Mustafa's Learning from Data. I don't think it only applied to single hidden layer networks, but I may be wrong. Additionally, the book said the VC dimension is infinite in the general case.

I asked the question on CS stack exchange and no one took issue with the statement that DL had such a large VC dimension. The only counter response was that it didn't matter in practice due to DL's good error scores. But, that still doesn't mean DL is generalizing. Good error is only a necessary condition for generalization, not a sufficient condition.