I think there is some ambiguity on who can gain Suppression tokens. When discussing gaining Suppression, the Rules Reference uses the term "unit." But when discussing the consequences of Suppression it either uses the term "troopers," or (in the case of Panic) refers to "units" which are usually immune to the effect. So, as far as I can tell, there are no consequences to having suppression spelled out for non-trooper units, but non-trooper units are not explicitly excluded from gaining it.
Should I just not bother giving non-troopers suppression? Or am I missing something?