~long story with mixed up terms ~
No, you seem to misunderstand money and Bitcoin too.
Shortly, your long story is like telling that Puma is counterfeit Adidas.
However... let me show you how we stay.
The definition of money is
something generally accepted as a medium of exchange, a measure of value, or a means of payment
And fake means counterfeit. You know, for this you need the original thing to copy/fake it. And exactly the miners you blame and also all the full nodes over the world ensures that "counterfeit Bitcoin" cannot exist.
If you hack your bank and put some additional zeros to you account you basically counterfeited digital dollars, but no original thing to copy it existed. So given your logic it is impossible to make fake digital money. This is obviously absurd. Fake money is the one that is intrinsically worthless and is put into circulation with the intention to extract real money, goods and services from other people, without providing these people something valuable in the future.