I never laughed at this, it's not strange that there are words or word forms where the only difference is a single phonetic feature, or indeed where there is no difference at all. As you say that is the case in all languages.
And regarding accents in Greek, I don't recall encountering any case where the position of the accent was the crux. Which isn't really surprising given that the texts didn't have accents originally, so the writers couldn't rely on that alone.