It makes no sense in terms of game rules.
Attachment card types are attached during the planning phase by the player.
Player cards from player deck are attached to Elder Things when they engage, and by sharing the same word "attach" - it's a completely diffrent mechanic, attaching all - events, attachments, allies. And in this mechanic card text doesn't matters, the only thing that matters is cost.
Only the player is restricted to the planning phase when playing attachments. The encounter deck isn't.
Example: "Caught in a Web". Counts as an attachment, is attached during the quest phase.
The card text of Forest Snare gives no limitation either. It just says "Attach to an enemy engaged with a player. Attached enemy cannot attack." All these requirements are fullfilled when a Nameless Thing's forced action triggers. I still have no clue if this was intended or not. After all Imladris Stargazer gives the player a good chance to actually trap one of these monsters with Forest Snare.