Can somebody explain this answer (apparently) by Justin?

Q: In Honor Among Thieves E2, does Raythen's Investigate apply when he checks an objective token that is revealed to be a search token?

A: Yes.

https://boardgamegeek.com/article/12990717#12990717

Investigate is a special action of Raythen (ally) that targets a search token. An objective token in this quest is revealed by using an action (not a special investigate action). After the objective token is revealed to be green, it is discarded. Where comes Investigate into play here?

Ability text:

Investigate : If this ally is adjacent to or in a space containing a search token, the hero closest to this ally (of the heroes' choice) is treated as if he performed a search action. That hero may reveal the search token and draw a Search card as normal.

In that encounter, Raythen can reveal objective tokens (as can the heroes). If the token he reveals is green, it's treated like a search token (that is, the appropriate action is to discard the token and draw a search card for the hero who revealed it). However, Raythen (beling an ally) can't hold search cards. Therefore, if an objective token he flips turns out to be green, then the search card would go to the nearest hero, as per the investigate ability.

I see, I was thinking that investigate could only be used for search tokens not for objective tokens. The quest does not even specify that heroes reveal objective tokens with search actions ... Could Raythen investigate a challenge token, too?

No. Normally, Raythen cannot even investigate objective tokens. The question is only in reference to how to handle this specific quest's mechanic which otherwise would allow Raythen to reveal a search card.

In other words, for this encounter, the green objective tokens end up being treated like search tokens, so flipping one is handled the same way Raythen handles search tokens- with "Investigate".

Found it in the offical FAQ. Raythen is using a Special Action (not Investigate) to reveal objective tokens. If he reveals the green token, the closest hero draws a search card. The FAQs do not even mention Investigate. I am content with this solution.