Fish like many other animals can have their growth stunted by stressful conditions, such as lack of food or unsuitable living quarters. Think Roumanian orphans. Not something you would want going on in your tanks, certainly.
Different fish are affected differently by lack of living space. Some can get their growth stunted (probably as the result of stress), others die, some just get nervous and aggressive. Depends on the species. But you do see enormous plecos in tanks where they can't turn around- it's horrible. What will not happen is that a fish can learn to live comfortably in a tank too small for it. That is indeed an old wive's tale.
