scottindeed said:
With the Shadow Card that makes you discard an attachment, I would argue you can get rid of Caught In A Web. On p25 of the Rulebook: "Players always assume control of Attachments that have been played on their characters".
Yes you would argue but this has been argued before. A card that comes from the encounter deck is never considered as "being played" or "played". Only cards that comes from player's hands can be considered "played". So you do not control Caught in a Web. This is official.

