Usually Falco would just side B into the stage and die from that low though.
I'm pretty sure it had to his horizontal distance from the stage when he Phantasmed, because we found out that Falco doesn't exist within the first 1/3 or so of the attack, which is why it does crazy things with the ledge (and goes through attacks).
I really think from that particular height anything would have grabbed the ledge. I'm not sure how Falco Phantasm involving a teleport would explain anything. His horizontal distance was obviously important because it put him within ledge grab range, but I am just not seeing what's supposed to be special here. This was a pretty ordinary ledgegrab other than the fact that it was probably at nearly absolute max range. The reason you don't think ledges have that big of detection is probably because of the hardcoded rule against regrabbing a ledge shortly after letting go of it.
Also, I am pretty sure I understand the mechanics of Falco Phantasm (and Fox Illusion), and it's pretty non-intuitive. In the case of Falco Phantasm, Falco first creates a series of projectiles in front of him (they are non-reflectable and visualy are the blue outline Falcos). These can hit and are the damaging part of the move. Then Falco moves forward. Fox Illusion is just the opposite. Fox moves forward and then creates the projectiles where he just passed. This is why Falco Phantasm is so much higher "priority" than Fox Illusion; it sticks out a hitbox without Falco even being there to take a blow. I haven't studied it carefully, but I do not believe either of these moves inflict hitlag on the users when they connect. That would be supporting evidence of what I'm saying. Of course, these moves execute quite fast so they can be quite confusion.