Could you be more specific? Exactly what part is not true?
You don’t understand the basics of what the Fed does and your post is a mess of misinformation. The Fed gets its income from its holdings of Treasury paper, not by means of your mythical “interest payments” from lending to member banks.
The interest payments that the Fed receives are the same as what you get on your T-bills, the sole difference being that you get to keep all of the money that you receive in interest and the Fed has to turn over to the Treasury all income exceeding payroll and basic expenses.
The “lending” to banks that you imagine you see is the Fed exchanging dollar credits for debt paper held by banks. This is the Fed adding high-powered money to the banking system in place of illiquid debt instruments, so that banks will have money that they can lend instead of having their funds tied up in T-bills or old loans.
In reverse manner the Fed also drains high-powered money out of the banking system to curb inflation. It sells its holdings of T-bills to banks to convert high-powered money into illiquid T-bills. In your scenario this would end up being some kind of “reverse interest” since it amounts to the Fed “borrowing” from its member banks.
Of course there is no real borrowing or lending in either case, it’s just the Fed adjusting the level of high-powered money in the banking system.
And as for the “2 1/2 TIMES” multiplier that banks can lend on the money they get from the Fed; the multiplier is actually good deal greater than that. That’s why loanable funds in the banking system are high-powered money.