Yes, I think you are correct about the HC (High Capacity) part.
I know for a fact that you can use a class 2 in your phone and it will even allow for 720p HD video recording (which is the most daunting task a phone can use it's flash rom for).
I have a Motorola Droid X and it came with a 16GB class 2 card which works awesome. I bought a 32GB class 2 card for it and that too works above my expectations.
The class specifications on SD cards are a minimum performance requirement (that doesn't mean it will ONLY perform at a certain rate). The only reason why you might need more than a class 2 is if you are a professional photographer using the card in your camera, or maybe you are a high end gamer using the card as flash for your computer. As for phones, I don't even think the data transfer buss on even the smartest phones can go faster than class 2, but I might be wrong.
I have noticed that every class 2 (SanDisk) card I have, 1,4,8,16,32GB all perform at about a class 4 rating. This isn't a guarantee, but it seems to be a norm when buying a reputable manufacturer's product from a reputable seller. I only buy SanDisk, and I only buy from vendors that are well known and have great return policies.
There have been some illegitimate sales of 2GB cards being marked as 32GB... one way to tell is if the card has a serial number printed on the face.
If you still want that added performance of a class 4 card then good luck, there aren't many out there and when you find one it will cost a fortune.
Verizon has a 32GB class 2 for 99.99 or maybe 89.99.