That's a technicality in my opinion. If the website owner would ask you to fix it that would be one thing, to hack them and then to 'offer to fix it' (presumably for a fee) is across the line. It's a fine one but it's definitely there.
Hacked a site?
Send them a message about it, give them time to respond and time to fix. If they don't respond after a reasonable time has passed go public with it, don't try to translate it in to paid work.
Trying to turn a PoC into paid work is indeed sketchy; but I do understand that security researchers/whitehat hackers would like to get paid for their work.
It would be good if more companies set up bug bounties, and even better if they'd set the reward a bit closer to (reputed) black-market prices.
Hacked a site?
Send them a message about it, give them time to respond and time to fix. If they don't respond after a reasonable time has passed go public with it, don't try to translate it in to paid work.