That's half correct (and yes I did leave that bit out as a simplification to the argument), banks do create money, but not in the mechanism called "fractional reserve banking" which is only found in textbooks because it would actually violate accounting rules (it's true that banks only hold a fraction of their assets as central bank reserves but the mechanism referred to as "fractional reserve banking" and related "money multiplier theory" can't work because the bank can't make a loan out of a deposit because it would require two entries on the same side of the balance sheet).

But it is true that when a bank creates a loan (which to them is an asset, but to the borrower is a liability - debt) it creates a matching deposit (a liability to them) which does increase the money supply. The amount of central bank reserves is not hugely relevant to the process, that's more of a liquidity management thing. The main limitation is actually capital adequacy regulations.

But all of that aside, a Government doesn't need banks to create money so they can tax it, it permits banks to do it by granting them a banking license.