This 100%.If I had to guess, I'd say the writers probably didn't worry about it that much. Injuries on shows are frequently dismissed like this. I can't actually remember a show other than Dexter where a main character was in the hospital for more than one episode, even with what should be severe injuries.
Every time I complain about something similarly ridiculous, my husband says "it's a movie" or "it's a tv show." And yeah, they don't bother themselves too much with reality, as long as they can keep people watching.