Both, but for two separate reasons.
We can't do automatic billing via PayPal because they don't allow us to "pull" money from your account — PayPal only allows payments to be made by you, the user, clicking a link, logging into your PayPal account, and clicking "make payment". So, it's not something we can make happen automatically.
That being said, if you want to pay for your account renewal using PayPal, that's fine! You'll just have to do it manually through the panel, before the account renews automatically using your credit card. We send you a few emails warning you before we rebill you, so you can use those as a hint.
You can't pay for a domain "on the spot" using PayPal because the payments don't always go through immediately. They usually show up in a few seconds, but it can sometimes take a few minutes (or longer!) for the payment to appear and be credited to your account, and we can't be sure you actually paid at all until that happens. Since we need the payment right away for services that cost you money immediately, like domain registrations, we currently restrict that to credit cards only, since we always know immediately whether those went through or not.
PayPal's policies on this are pretty vague, so I really can't say for sure. Please contact DreamHost Support with details.