poppa bar abba – there are many stories of Hashem “not answering tfilos” bmaase nisim? In oomis’s case, she was davening for Hashem to change tevah for her to an extent. Her children’s lives were going along a cetain line in tevah, and after she davened that teva was distorted for her. If the tevah you were hoping to change through your tfilos IS changed, it can only be because of the tfila. Meaning tfila works. The opposite logic would only make sence if Hashem actually made a nes to not to answer your tfilos.
I am not saying that this reasoning works with tfilos that stay within teva (though if Hashem can answer a big bakasha like that of course He can answer “easier” ones too). In conclusion, I think oomis had a point in saying her story proved something.