I appreciate that you posted the images! Otherwise I have to look them up.
That's an interesting line of reasoning. The question is, does Lantern modify Border Guards (thus the Estate with the token is modified), or does it modify the playing of Border Guards (thus Estates aren't played differently). The rulebook doesn't lock in an answer.
I don't think your alternate wording is the way to think of this; sure if I saw that there was some confusion to clear up and it was so worth clearing up as to mangle card text, I would have mangled the card text to make it clear, caring only about clarity and not about what the ruling would then be. It wasn't trivial to word though and your wording is not dazzling me.
I feel like the text looks more like shapeshifting than when-play-modification. Man that makes Lantern a 4th shapeshifting thing that doesn't change all cards with the same name at the same time, along with Band of Misfits, Overlord, and Inheritance. That weird thing majiponi found may be doable with Lantern too (or, might be doable if certain utterly innocent cards existed). It should say, "During your turns, Border Guards reveal 3..." Damn.
I am tentatively going with you and reversing that ruling - to, Inherited Border Guards benefit from Lantern. Let's not ask Stef to change it just yet. Maybe some people want to weigh in on their intuitive reading of Lantern.