Do cows actually have problems where they can expand like that?

They most certainly do. It has to do with eating too much green food like legumes, clover, or alfalfa, which ferments and puts off a lot of gas. Normally that is dealt with by belching, but the gas can also get trapped in part of the stomach. They can die within 3 hours if nothing is done. The quickest treatment is to poke a hole, preferably with a tube inserted so the gas can continue to escape.
It's called ruminal tympany, also known commonly as bloat.