More importantly, that's over the network so you have to trust the site to not log what it gives back, every CA to not have issued a false cert for them (allowing them to be trivially MITMd), and all software that runs on your computer to boot.
The "PRNG" vs "Real RNG" boogeyman scare is such a load of horseshit.
The whole point of modern PRNGs is that they're good enough computers can't detect patterns. I assure you that you're gaining zero security by using random.org vs openssl rand... and in fact, you're losing massive amounts of security because it's going over the network.
Minor nitpick: you should replace "PRNG" with "cryptographically secure PRNG". Not all PRNG methods are aiming for the standard of "computers can't detect patterns", for example the common Mersenne Twister PRNG would not be a good choice to generate crypto keys or passwords.
You're right that using an internet service like that to generate passwords is insane, and there is no need for some fancy custom RNG hardware just to generate some keys/passwords.
The "PRNG" vs "Real RNG" boogeyman scare is such a load of horseshit.
The whole point of modern PRNGs is that they're good enough computers can't detect patterns. I assure you that you're gaining zero security by using random.org vs openssl rand... and in fact, you're losing massive amounts of security because it's going over the network.