When you generate the address you get the addy and the private key, so, to get access to the coins you should import the private keys to any wallet. But the problem here is ¿Why you make an address on an online site? that's one of the biggest mistakes you can do because the site can save the keys, or a MITM attack could take the keys when they were created. The right way to make your own paper wallets it's with vanitygen. That's our best option.
... No.
Where do I start?
1. They downloaded the website and used it offline. This is stated in the OP
2. That's not what a man-in-the-middle attack is
3. Vanitygen doesn't let you generate paper wallets per se. They're vanity addresses. From there you can choose to create a paper wallet, hot wallet, import it into a hardware wallet or anything else. Using vanitygen is only more secure if it's on an air-gapped computer.
Of you're going to buy a bitcointalk account to shitpost at least get the basics down.
OP I'd be happy to help in whatever way I can. I used bitaddress to create many paper wallets and always without issue. As others have stated please make sure to double check every address type. Legacy includes compressed or uncompressed. Both of these would show up on a bitaddress paper wallet.