The puppetbot are not allowed to be in a fireteam. Exile only works against Fireteam. It does not work against G:Synch, G:Servant or G:Marionette. You can see here for the types of Fireteam : http://infinitythewiki.com/en/Infinity_Fireteams And you can see here for the exact list of all the fireteams that could exist : http://infinitythewiki.com/en/List_of_Fireteams Exile can target a Securitate who's in a Fireteam, as Securitate can be in a Core or Special fireteam, but puppetbot can never be in a Fireteam. While Troupe borrows segments/fractions of the Fireteam rule, you'll notice they had to retype several into the marionette effect, that is because Marionette/Troupe is not an actual fireteam. edit - as the other thread pointed out, Number 2 is worded the same way, and definitely is intended to work, makes a case then that troupe is a new fireteam type (and that half the bullets in Ghost are actually redundant as they re-affirm fireteam rules that are already applicable as troupe is a new type of fireteam).
Parts of the rules are retyped because of the Controller. Not because the Puppetbots aren't in a Fireteam.