I think the actual answer is this:
1) Yes, they were afraid the backlash wouldn't be worth it. It has been obvious they are embarrassed of what DOA has become since DOA5 tried to rebrand the series, failed miserably, and they made hot bank on appealing to the audience that wants ass & titties. They're a company, this makes money, they're going to pursue this where it makes sense to do so, and it doesn't make sense to do so in America because it is culturally different.
2) They wouldn't care about the first one if it was going to do well. It's not. It'd sell fucking terribly and probably will sell fucking terribly when it comes out. The PS4 audience isn't the otaku audience here and the Vita audience isn't big enough to care about. You know what the main driver behind this decision is? It's not DOAX3 itself, it's probably Toukiden, which they openly admit greatly disappointed them. They have assumed before that the Vita and PS4 audiences overlap in the west, and this is very much a Vita audience game, and that assumption has burned them.
They're concerned about 1, but they wouldn't care if it would sell well. They have outright said as much. They would bring it over if there was demand, there is no demand, so they're not bringing it over.
Which brings me to what I think is happening now, 3) they're just making excuses. This clears them of any anger, it clears them from having to make a print run from a game that stores won't want to buy, that will distract from their DLC money makers of DOA5 and Core Fighters, and will be an annoying albatross around their neck when they decide to bring out DOA6. They're also not ignorant of how the eSports scene views DOA and how they outright ban costumes and can't get the game to EVO because it's just Anime Titties: The Fighter to most people. The DOA5 in-game ticker mentions every weekly tournament in someone's boys and girls club rumpus room, so they're fully aware that this strategy is not doing them favors in America. The guy at Koei Tecmo said what would quickly solve his problem, realized this does way more harm than good, and quickly deleted it.
They're trying to cover their own asses, Play-Asia took advantage of it, and now it has become a shitstorm.