Anyone can write down a number a name of a non-existent thing and then clam to owe it.
Yes, but that won't be necessarily true. For example, you can tell me that you own 1 BTC (the fake number as you say), but if you don't provide me a valid signature which proves that you're the owner of the
outputs, then I'll have to keep your word for it. So it's not the same as having a ledger which can be altered by anyone.
It is obvious that you don't know anything not only about Bitcoin, but about cryptography in general.
Satoshi, via his software, can write down that a miner's address owns 10 bitcoins.
But, that won't make it true, because they won't be able to provide the valid signature.
You're wrong. Learn to admit and move on.