Trust me, it is 100% that your private key is publicly known and is in this database.
No, it isn't. This database is generating keys on the fly as each page is loaded. If it were to generate all keys, it wouldn't even be able to generate a tiny fraction before the heat death of universe. Hell, you couldn't even
count the number of keys (just short of 2^256), let alone generate them or check for a balance, before our sun burnt out.
The chances of winning a lottery are in the range of 1 in 10^6 or 10^7. Given that 2^256 is approximately 10^77, you are more likely to win the lottery more than 10 times in a row than you are to stumble upon your private key on this website.
Whether the system computes them or recalls them from memory is totally pointless. ALL the private keys are accessible via that URL. Why do you somehow think you are more protected because the system generates the keys rather than recalls them? The dumbest fucking argument ever.