You could as well say that Will would have never existed, there would only have been Tom. Only he wouldn't have been using the nickname Tom. It makes as much sense as the other way round.No, actually Tom's parents are responsible for his existence. The transporter accident is only responsible for him having spent 7 years alone on the planet, coming back to see that there's another version of himself with a higher rank and a far more eventful last 7 years, and adopting the nickname "Tom" instead of "Will" to distinguish himself from the other version of himself.Well, maybe Tom didn't mean to be that bitter. O'Brien was, after all, a transporter chief, and a transporter problem was responsible for Tom's existence in the first place (even if it wasn't O'Brien himself). Maybe Tom just hates transporter chiefs and lashed out in anger?
But without the transporter problem, Tom would never exist. There would only have been Will. Mr. and Mrs. Riker are not responsible for what happened to Tom, because they only had one son - Will. Tom's entire existence is directly attributed to the transporter mishap - if that had not occurred, there would be no duplication of Will, and therefore, no Tom.
Tom existed from the moment when he was born, as William T. Riker. So did Will. They just used to be the same person, until the transporter accident. Beverly explained it in the episode itself, so I don't know why people get confused about it: they are both the real William T. Riker, only with vastly different experiences during the last 7 years. Viewers seem to react to Will as the "real" one, and Tom as someone who didn't exist before the transporter accident, but that's simply not true.
Even though adopting the nickname "Tom" was a way of distinguishing himself from the other Riker, one may also say that Tom, in a way, accepted an inferior position by choosing a new nickname for himself, as if he wasn't the same William T. Riker who had finished the Starfleet Academy, served on The Pegasus and had a relationship with Deanna.