Well, not really.
I (and two others) signed cheques on an account that I wasn't a signatory on for 3 years. We only found out when we went to change the signatories again, and found out the previous mandate hadn't been processed! Apparently they only check the signatures against their records if the cheque is over an unspecified value (which they wouldn't disclose for "security reasons", hah!) or if they have other reasons to suspect suspicious or fraudulent activity on your account. And there are numerous stories about banks paying cheques into accounts other than the one that they've been made payable to, as they don't properly check the details on a cheque.
To be honest, I have never assumed that they did check the signature.
And if banks pay money into the wrong account, with a cheque there is an audit trail. That cheque says who that money was supposed to go to. If the bank screws up, it's not me that's at fault. I have written the cheque correctly. My responsibility basically ends (unless - of course - it's a cheque going to an account I am responsible for.)
But if I make a typo on online banking, and the money goes into the wrong account, then that is my fault. There's no checking or confirmation done by the bank. They don't even check the account name matches between the destination account and what I have put. If I mistakenly transfer a huge amount and it goes AWOL due to a mistake, I'm screwed.
Of course the answer is to do a token transfer first, confirm recipient has got it, then do the remainder. But it's faff and it's hassle for everybody. And it's a fudge to work round the fact that the system is fundamentally flawed.
I use online banking all the time. I've used it for easily 15 years. But I still distrust it.