I don't know how the criteria is applied in other states.
Here's an example from Michigan: A few years ago, my brother had a medical emergency that caused his complete and permanent disability. He can never work again. While in the hospital, social workers got him signed up for SSI, and also for Social Security Disability. The SSI process is much faster, and he got approved for that right away. His monthly check from SSI was about $600 a month. One of the stipulations with SSI is that it automatically qualifies the recipient for the maximum $200 in food stamps. It's automatic -- you get approved for SSI, you get the food stamps. And full Medicaid coverage.
Eventually his application for Social Security Disability was approved. At that point, the SSI stopped and the SSDI began. His SSDI check was a little over $1000 a month. Better than the $600, BUT... the loss of the SSI and its automatic qualification for food stamps meant that my brother now qualified for what the state of Michigan determined was appropriate on a monthly income of $1000. His food stamp allotment was cut to $47 a MONTH. This was for a man with NO assets -- he did not own a home or a car, had no cash in a bank, no IRA, nothing. He was expected to pay for rent and all his living expenses, including medical visits and the medications he needed to stay alive, on $1000 a month with $47 help in food stamps. That same $1000 a month also disqualified him from the automatic enrollment in full Medicaid that he had also received on SSI -- Michigan decided that he now only qualified for a "spend down" amount of over $600 a month, meaning that Medicaid would now only pay for any expenses -- including medications -- over and above the $671 that he would have to spend out of pocket first. Per month.
So he was left with having to pay over half his income in medical expenses per month just to stay alive, but even with all that only qualified for $47 a month in food stamps. There was no way he could do that, so he moved in with me. After two years on SSDI, he became eligible for Medicare. He pays the premium out of his SSDI every month and now his medical care is largely covered. Michigan's answer to that? Now that he doesn't have as much medical expense, his food stamp allotment was cut to $16 a month. He told them to cancel it... give the $16 to someone who needed it more. He still lives with me.
Each state has to comply with some federal food stamp rules -- the $200 for SSI recipients is one of them. But each state can also set their own criteria for its citizens that fall outside the SSI protections. Arizona's typical payment of $29 a week probably means that the people receiving that amount have absolutely nothing else and have a very, very low monthly income, less than my brother's, I imagine. They probably have no other money to supplement that food allotment with. That $29 a week is... it.