Your available credit line is not debt, and I can't recall ever hearing of anyone being held accountable for fraudulent purchases made against their account. Does this happen?
Here (Singapore) card conditions were recently changed so that you would only be liable for the first $100 of fraudulent transactions (assuming you can prove it wasn't you). I think the bank can still hold you liable for more if they find you were negligent about guarding your card details.
Prior to these condition changes, I remember being told by the bank that you would be liable for all charges incurred before you had reported the card physically stolen or lost.
I wound up being held accountable for a small amount because I missed a deadline in the follow-up paperwork. So yes, it happens, but only when it doesn't matter much.
In that your credit score has a factor of actual debt to total credit. Someone with $1000 of debt on $100,000 in credit is much better off than someone with $1000 of debt on $5,000 of credit.
So things like car loans and mortgages could be bad, since they start at 100% and go down.
Credit utilization is another element though. It's bad if you have too big a line of credit, but good if you have a historically low ratio of (debt/available credit).
"A credit card would give me the ability to instantaneously take on $10,000 in debt. I don't want this." is a responsible and admirable position for someone to take.