So of course tomatoes eaten directly off the plant are gonna be "superior" (I personally prefer them a bit cold but that's just preference), storing tomatoes like potatoes or onions is just completely incorrect if mostly because when you tell people to do that, they're gonna immediately go to stick them under their sink. While potatoes and onions do well in cool dry storage, they still have a resistance to temperatures above what anyone should be storing tomatoes at.

While it's correct to state that tomatoes shouldn't be stored at temperatures below 40°F, saying "don't refrigerate tomatoes" is complete BS. Most refrigerators aren't cooling down to the 30 range, and even if they are your tomato is still gonna do better there than in is on your shelf if you're trying to keep it for a longer period of time.

That being said, if you have a tomato that you want to ripen a bit, store it out of the fridge on your counter, it will help it out a bit. But as for a ripe tomato? Keep it in your fridge. We pick hundreds of pounds of tomatoes a week at my farm, most of them are sold only a day or two after picking at our farm stand, but we still have to refrigerate them over night because if we don't, they will turn to shit, and no one is gonna pay to eat a shitty tomato that's been festering overnight during a hot summer, especially if you live in a humid area. Potatoes and onions on the other we leave out overnight and they do fine for days without any discernable difference.

Refrigerate your tomatoes, keep your fridge set to a reasonable temp (40-44°F), do not treat your tomatoes like onions or potatoes.