Ok I've tinkered long enough to figure out what causes it, much as OP has done.

I found that the playable unit needs to be from the same faction as both your OPCOM module and your military logistics pool module.

Take for example you're playable unit is from massi's uk spec ops pack, then your OPCOM modules needs to be controlling mas_uk_sftb and your military logistics module needs to be set to supply the same.

Essentially, just being on the same side isn't enough. However, ones you get it working by meeting the above conditions, you can set your player logistics to "side" and you'll be able to call in re-enforcements from other factions as well, without listing those factions in the modules (if my memory serves me correctly).

I also have this issue. Has anyone found a fix yet?