Maybe someone from the PI is better equipped to answer this, but here is what I understand.
1) Remy started using belts to more closely resemble the Japanese arts that had become so much more popular than FMA, giving people what they expect from a martial art. The same with the forms, I would guess. So as far as tradition goes, the red border can't be that old... Most FMA do not use a belt system.
2) I've read (Mark Wiley's works) that notable eskrimadors in some parts of the Philippines would have their status denoted by wearing a red headband or skullcap.
3) I've also heard, though I don't remember where, that originally, the red border was to be extremely thin at lakan, widening at subsequent ranks, until the entire belt became red at 10th degree. Apparently, that idea was scrapped at some point.
Honestly, though, I never talked to the Professor about it, and can't confirm any of this as fact. Just repeating what I've heard!