I have a different understanding of how SSI is administered. I have never heard that the feds give hunks of money to the states to pass out to those approved for SSI. There are SSA offices all over the country, and those are operated by the federal government (I think.) The SSA, as far as I know, send the SSI checks to individuals all over the country. If a state wants to add to that amount, it has two options. It can set up a system for sending it's own checks to citizens, or it can give the money to the feds who will distribute it on behalf of the state putting the money right into the SSI check. Here us a reference I found:

Who Administers the Supplement

The Social Security Administration administers the state supplement for some states. The states with Social Security-administered supplemental payments are: California, Delaware, District of Columbia, Hawaii, Iowa, Michigan, Montana, Nevada, New Jersey, Pennsylvania, Rhode Island, Utah, and Vermont. You can see the state SSI supplemental amounts for these states on the SSA's website. In these states, your application for SSI is an application for the state supplement as well.

In states that administer their own supplement program, you have to file a supplemental application with the state agency. You can find the amount of the supplemental payment for all states in our state-by-state disability pages.

What Are State Supplemental Benefits for SSI Disability? | Disability Secrets