I won't comment on Amazon shopping around for tax breaks, but I would take issue with idea that welfare payments "subsidize" Amazon.
The whole idea that public assistance subsidizes employers is based on the false assumption that people only require to get paid what they "need" and therefore accept lower wages because they don't need as much due to government aid.
I think a more plausible explanation is that employers pay employees based on productivity and supply of employees with that skill set. If an employer can make $15 an hour per marginal employee, then that employer will not pay more than $15 an hour, regardless of what employees demand. And if there is an oversupply of employees with those skill levels, then they can choose from the pool based on the market rate. This is pretty standard economic theory.
Another way you can think about it is that Amazon is helping states and federal government by paying these employees, otherwise the welfare payments would be higher.