I don't know if this is called "invisible pick up" or not, but it may. It is also referred to as "pick up and knit" sometimes. I wouldn't say one way is the only way to do anything in knitting. I know you can pick up from left to right as well, but used to think that was impossible. LOL
Do you pick up stitches for your mitten thumb? Is so this will work. If you don't have a piece of yarn where you will pick up stitches, just hold your new strand of yarn behind the piece you are picking up from and when you stick the right hand needle into the stitch, just pick up that new strand and keep going from there.