Most of the time, being invisible is an obvious advantage when using the Stealth skill. So why doesn't the Invisible status (or the spell description) just say you get Edge, and take GM discretion out of it?
A couple of examples involving Invisibility and when it's clearly not "Edge-worthy" on a Stealth roll:
When you're sneaking past a blind/blinded person, being invisible is irrelevant.
When you're sneaking past a person with no line of sight to you (other side of a door/wall, etc), being invisible is irrelevant.
You're using the Stealth skill to perform some Sleight of Hand legerdemain (if they can't see you, who are you impressing?)
Furthermore, there may be contexts where invisibility's benefit is diminished:
You're moving around through fresh snow.
You're moving around through water.
You're moving around through thick smoke/mist.
Some cases where the context of the observer's ability to see infrared may lessen the advantage of invisibility:
You're invisible, but you've been hiding in one place long enough for the surrounding objects to begin to heat up.
You're invisible, but the warm footprints you leave behind as you move around sure aren't.
You're invisibile, but certain critters "feel" infrared (pit vipers,
dogs, etc) rather than see it, and invisibility only works vs visual detection...
The longer you think about it, the more cases one can think of for why being invisible might not warrant the circumstantial edge point. Hence, the rule is "GM discretion". As with most Edge awards.