I think the wording on Lantern makes this less clear.
Border Guard by itself seems to suggest that you need to reveal 2 actions, because of the word "both". It's reasonable to see this as a different wording of "if you revealed 2 actions, take the Lantern or Horn."
However, Lantern says "it takes all 3" in parenthesis; which suggests that it's not a rule change but an explanation. If "it takes all 3" is indeed not intended to be a rule change, but a rules explanation, then that would suggest that Border Guard really means "if all revealed cards are actions".
So the 2 options as I see them:
1) Border Guard means to say "if you revealed 2 actions", and Lantern intends to say "Border Guard now says 'if you revealed 3 actions'". If this is the case, it seems wrong for that text to be in parenthesis.
2) Border Guard means to say "if all revealed cards were actions". This is consistent with the way Lantern suggests, but it doesn't seem likely that it's the intent.
*Edit*
Lantern reminds me of
Experiment here. Lantern tells us
that it takes all 3 being actions, but it doesn't tell us
why that's the case. Like how Experiment tells us that the second one doesn't come with another, but it doesn't explain why that's the case. So why does it take all 3 being actions? Is it because Lantern has secretly introduced another wording change to Border Guard that's not specified? Or is it because Border Guard was always "all" and not "both"?