Or is it just because CC stop at the upper limit and debit cards tend to take people past overdrafts?
Mostly this and the fact that one is an immediate payment, the other a deferred payment.
Because a debit card is linked directly to your bank account, billing errors can put your account immediately into overdraft and incur penalty fees (which can quickly escalate because repeated billing errors will also incur repeated fees). Banks will not refund these fees until whoever caused the billing error has reversed their transaction(s). This leaves your bank account in an overdrawn (and often frozen) state until the situation is resolved, which could take days or even weeks, with obvious implications for things like mortgages, rent, bills etc. EA/Mythic have moved reasonably quickly and most people have seen reversals within about 2-3 days, but their legal obligation is 30 days, so a less scrupluous company could really drag their heels on putting things right and still not fall foul of the law.
A credit card on the other hand means you have a minimum 30-day buffer to get things sorted out before any charges start to be incurred. Also, there is a lot more legislation in place currently to protect credit card owners against fraud compared to debit cards (though if your debit card is Visa then you have a higher level of protection).
In short, using a credit card gives you a buffer zone against problems whereas a debit card exposes your bank account directly to any potential problems.