No, I think we're talking about exactly the same thing. And you're also right that the theory is that raising the reserve requirement shrinks the money supply.

Wikipedia claims in the US the reserve requirement is 10% for demand deposits and zero for time deposits. Now, how is the theory

The reserve requirement can affect monetary policy, because the higher the reserve requirement is set, the less money banks will have to loan out, leading to lower money creation, and maintaining the purchasing power of the currency previously in use. The effect is exponential, because money that is loaned out can be re-deposited; a portion of that money may again be re-loaned, and so on.

compatible with my argument above that

in order to cover 100 worth of deposits you have to repo 105 worth of eligible assets.

The bank balance sheet could well consist of an additional 100 worth of debt on the liability side, 20 worth of equity, and 115 worth of other assets, which may or may not be eligible collateral for repos. To wit:

Assets			| Liabilities
======================================
eligible assets 105 + x | debt	   100
other assets	115 - x | deposits 100
			| equity    20

I fail to see why requiring that 105 worth of eligible assets be pledged at the discount window in exchange for 100 in cash would collapse the money supply.

Maybe it's that the standard theory is bunk, but I'm reluctant to claim that just yet. The wikipedia article has interesting cross-country and historical data on reserve requirements...

Economics is politics by other means