Yeah, I kind of agree with your semi-sarcastic take. While that salary is well above the US average, the fact is that they almost certainly don't make enough to own or rent a home in DC, and a second home in their constituency. It all but ensures that there can't be an honest member of congress, unless they feel like sleeping in their office.
What can Congresscritters expense? I'd assume they need to travel between their home state and DC frequently. Would lodging for work where they do not have a home be expensable somewhere?
Isn't the solution to needing two homes to do the job for the government to provide that as a work expense rather than permitting funky financial hijinks?