Not really the subject of this thread , but I thought the Englund has been proven to be better (if not winning) for White. The Budapest though has so far not been refuted and is actually played by some GMs .
Yasser Seirawan on YouTube says it's quite playable for Black.
It is winning for white, but figuring it out over the board isn't easy for a beginner.
Maybe a beginner first has to lose a game against this gambit and then find out (learn) how to face it a next time. The problem with gambits is that they require a special (direct) treatement where any knowledge of the basic strategies just fail.
But how many beginners can prove it's bad off the top of their head? And I've never even heard of Fajarowicz or 4.a3. Sure you could memorise it but months down the line you may not remember any of it. At least with e3 you get a normal position and don't need to know any tricks.
Playing e3 is not trying to refute anything.You are just being lazy and allow Black to gain an edge.