Leo says it's unlikely the battery damaged the laptop, and it sounds like HP is just using that as an excuse to wash their hands of it. Having said that, third party batteries are dangerous because often they don't have the right circuitry and could explode. Leo recommends buying an HP battery and then sending it back for repair under warranty. Then they won't have an excuse to pass the buck.
It is possible that he did somehow damage it though, and HP has this on record so they still may blame it on that battery.