Economic theory says that interest rates fall in recessions. If they rise from risk then that defeats the theory. Why do ARM rates rise in recessions?
First lets correct some misconceptions "Economic theory says that interest rates fall in recessions." Economic theory (at least mainstream economic theory) does not say anything like that.
In fact in IS-LM AS-AD model, which is one of the workhorse models of modern macro, during recession if central bank would be passive and not do anything in recession interest rate would increase. This is because when an economy enters recession, demand for liquidity increases but the supply of credit decreases and hence ceteris paribus interest rate should increase.
Second, while adjustable rate mortgage (ARM) interest usually increases at the beginning of a recession it will usually quickly starts falling as data show. The reason for this is that in real world ceteris paribus condition is not realistic. During recession central bank will not be passive but it will actively try to stimulate economy by lowering its interest rates and by injecting extra liquidity into the economy which affect all other interest rates in economy including ARM and put downward pressure on them. Hence the interest rates will tend to eventually fall during recession as a result of central bank intervention if the intervention is successful.