i don't think that's true. i have multiple trees with only one space between them and my house and they grew just fine.
it might be due to them being blocked in by your flowers and paths? i would clear the area around them so they have one space clear on all sides just to get them to day 2, then see if they survive.
EDIT: actually you're right. trees in front of your house need to be two spaces from the house. trees in back like mine can be only one space.