Im a big modding guy for pc games. Ive modded tons of tattoos and faces and what not for both the nba 2k games and mlb 2k games on pc so I will try and explain how it works.
Players can be done numerous ways. Nba 2k does it this way. They have a 3d model for head and neck that is then "covered" by a flat image of the players face which would include neck tattoos. They also have a few different body type 3d models which include arms that are also covered by individual skins which include tattoos of the individual players.mlb the show doesnt do this.
Mlb 2k and the show do it the same for head and neck. For the body however they have certain body types just like nba 2k but instead of being covered by individual skins they are covered by generic skin tone 1 or skin tone 2 or 3 or so on. I know this because in mlb2k i made tattoos for my created player by changing one of the ingame generic skin tones and editing every other player to have a different skin tone. This way they only have to do 6 different arm skins instead of 2500 or however many players are in the game. In reality they could use generic skin colors for most of the players and different ones for players with tattoos but it still would be a ton of work.
Im gonna assume Yu Darvishs neck is because they use a generic 3d model for it. Hence why you say it looks like everyone elses.
I guess my point after all that lol is if mlb was concerned about tattoos so much it could easily be taken off the texture picture of the player. Im not calling anyone a liar but it seems more like an excuse because it definetly wouldnt be easy.