Wow. Now that you've spelled it out for me, I feel like an idiot as it is perfectly clear in the ruleset. I don't know why I thought all units lost a point of ELAN per turn.
If you want to make it clearer, maybe just add the word free to that first activation description. As in:
"Each Unit may take a single free action when activated.
A unit may roll against their own Elan to take an additional action, so long as their Elan is above 1."
Also I dont know why I spelled it ELAM. Apologies. And its origins make it very cool, I would never have known.