It's good phrasing. Most people probably wouldn't say, "Please, stay clear of the doors"..........they'd say, "Get away from the doors", or even just "get back".......................but it's understood what is meant when you hear "please stay clear of the doors" just like the student understood "mantengase alejado de los puertas", even if he/she wouldn't say it that way.
You're so right about differences in phrasing/vocabulary, Texan Mouseketeer...........I don't even think my students know the word "empuje" at all..................they all say "Maestra, estan pushando!"