I was reading an interview of a veteran producer/engineer and he was saying how he always delayed the overheads of a kit 20 ms.
What I don't understand is why he would delay the overheads instead of the rest of the kit (which I assume is close miced) since the sound waves will reach the overheads later in time and are essentially already delayed.
Any thoughts?

I would assume it's because after 20ms phase don't matter or near as damn it. It mostly affects frequencies outside of the human hearing range. Never done it with over heads tho if i've had to use ambients in a small room I have added a delay to give the impression of a larger one and to try and take it over 20 ms (you get a 1ms delay for each foot the mic is away from the source roughly so if I can get my ambient 10 feet away I'll add a 10ms delay and roll a little top end off).

i think you're thinking of delaying the ambient mics, but for what it's worth, i think adding 30-40ms of delay to the overheads (and mixing it back in to taste, probably not as loud/bright as the original overheads) is a good way to put some life in the cymbals of a dead room recording. try it.

while on the subject of overheads and ambient mics, it often sounds good to compress them quite a bit, with a slow attack and moderate release. Really squish them so that you don't have to use as much actual volume for them to show up in the mix.