Can you mess up the transmission by going over a puddle, is because it’s not going over 20 mph.
Usually not, unless you buried it in water and it gets inside the vent. Was it a big puddle??? Its probably an engine issue.
You’d have to drive through some very deep water to damage a transmission. What type of car is this?
My idea of a puddle is no more than an inch deep. How deep was your puddle?
You might want to tell us the whole story, but cause I don’t think you really asked the real question. Give us the whole story and does the other person have a different version of that story???