factually inaccurate
The confusion stems from the fact that there are two different services for Chase, one for check writing and one for debit cards. I am specifically talking about debit card usage and will edit my post to make it more clear.
Chase will charge you $10 per day for check writing overdraft protection on accounts that are linked, this is true. However for debit card use, you would be charge $0 if you opt-out and indeed pay $34 per transaction if you opt-in. The problem is that many banks combine checking and debit card usage in to one plan, and others like Chase split it up. My main point is that check writing is becoming very rare, and most people get dinged from fees using their debit cards. So if they are combined and you really don't write checks, then you definitely should opt-out.
There is $34 fee for debit card overdraft protection and $0 fee for opting out(here and here). Does this resolve your disagreement?
(The moral of the story: don't be overdrawn. It will cost you money in fees with or without overdraft protection.)
If you opt-out of debit card overdraft protection it will not cost you any money! If you opt-in for debit card overdraft protection it will cost you money. I know it sounds ridiculous, because it is.
Based on the links, Chase doens't even call their service for debit cards "overdraft protection," so this doesn't support the original point about words misleading people. Also, it seems that if you have debit card coverage and overdraft protection, you'll at most be changed $10/day for overdrawing with your debit card. Still better to use a credit card when you don't have money in your checking account, obviously.
(Also, as Louie Helm recently pointed out, as long as you pay your balance in full every month, you're better off using your credit card for everything because the rewards program will reduce the cost of everything you buy by 1% or more.)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.