Generally these days they are, but the problem is the money is removed is from your account by the time the charge appears, (at least a period of time), whereas on a credit card you have 30 days to review charges. This could cause overdrafts, etc. depending on timing and amount. Those too can generally be reversed, but the whole thing becomes more of a headache. I never use debit cards for any kind of recurring charges, and I avoid using them online in general.
The same is possible with a credit card - you can have your card maxed, get nailed with overage charges, declined transactions, etc. It's still a headache, but when I've had it happen to me I think I had the money restored within a few minutes of making the call.
