There are people who work who fall desperately below the poverty level, so this assumption makes no sense. I think many people here can tell you from experience that work =/= rich.
As far as the mechanchim argument, it may be less that you are working and can afford to pay more, and more that mechanchim are not typically paid very well AND they are performing a service to the community by educating our children. People may not always word it well, but that’s probably more of the attitude than the simple “you must be able to afford more.”