Perhaps this will surprise you, Putney, but other posters cannot read your mind to figure out why you said something. They can only read what you actually wrote.
So if you say "I assume the Troll Bash is an action and has the action symbol (arrow)….So, the bash is the Troll's one attack," then it looks like you are drawing an inference based on the implied rule "things that require an action count as attacks".
Similarly, if you say "I'm suggesting that the bash ability is an attack because it does damage," it looks like you're applying a rule along the lines of "things that do damage count as attacks".
If you want anyone that lives outside your head to understand your reason for thinking that Bash counts as an attack, you need to tell us what that reason is. We don't just magically know.
The way I read it, having the icon (which he prefaced by saying he didn't have the card to check) -- or the words "as an action" -- are a prerequisite for it being an attack action. All attack actions are actions, not the other way around. If the Bash ability was triggered by a surge, or other special event, it would not be an attack action. Damage from Lava is not an attack action, because it's not an action.
Assuming it is a member of the class "actions", how do you determine if it's a member of the subclass "attack actions"? Having those words on the card would be a pretty good indicator, but failing that an action that has the potential to cause damage would be an assault, but not battery if it missed. Whether all assaults count as attacks in the context of this game is the question. Not having the game with me at the moment, I can't find a specific example, but I think there may be some. Finding one exception would prove that not all assaults arising from an action are attacks, and would invalidate his conjecture.