A better wording would have been:
"Either +1 Influence or +3 Influence but you can not recruit units this turn."
At least that is how I understand the skill.
However, you ARE able to recruit units from non-interaction sources and still get the more powerful effect of this skill. One example would be using Call to Glory and healing during interaction. Another would be using Learning (which requires influence) and then defeating an adventure site that rewards a unit in that same turn. So your 'better wording' is inaccurate, albeit only in a few edge cases.