Now who are these five?
Come, come, all children who love fairy tales.
This makes no mention in which phase this applies in and as such would apply (for example) to reactivating a Panzer Tank unit during a battle in Phase 2 (Tactics Phase).
You are correct. This would need a clarification. The English text should be:
If [this] is in your Combat Zone, none of your deployed army cards reactivate during your startup phase unless you pay 1 supply point. During your tactics phase, you may trash 2 supply cards from your hand to thrash [this].
This situation came up in a game where a player had Old Man Winter applied and was attacking a City. The player didn't have spare Supply cards available during Phase 2 to trash Winter so it was still around during the battle. The player attacked with Tanks and wanted to use Motorcycle Messenger to reactivate one of the exhausted Tanks. Reading the English text as is on the Winter card implied he couldn't because he needed to pay a further 1 SP and he needed this 1 SP to exhaust the Tank for a second time.
As it wasn't the startup phase, he would not have to pay extra supply points.
I am deeply sorry for the disambiguity.