Hmmm. I'm afraid you can't transfer an action to Elder Thing. Having an action attached counts as being affected. By transferring an action to Elder Thing, you would affect it.
You're right! The transfer of Potion of Cowardice could not have taken place because transferring via Rules Lawyer "affects" Elder Thing even though I was transferring my opponent's card. Well it turns out I'm a cheater and didn't even know it.
I need to memorize the definition of "affect." It continues to trip me up.