We don't know for sure. There's a lot of precedence in older lists that seem to imply that keyword is only one way of counting fireteam purity. The white banner fireteam in white banner contains no units with the white banner tag. Obviously that could change, but as others have said, your suggestion that ONLY the keyword name of the fireteam matters adds extra info to track and complicates things. It is the opposite of the polish that is the theme of N5.
I disagree. It totally simplifies how you denote what makes team pure. Which in the new video today Carlos stressed even more but sadly still didn't clarify anything. But I also hear Killian say something about BAIR not getting full bonus in a team but still very good. Which he is. That guy is going to be a huge pain in my back area. Literally. Anyway, I'm not going to say anymore about the fireteams until we see full rules. We shall see.
Black AIR + Killer Hacker + Parachutist(Deployment Zone) is a very good profile too... not with a great weapon (SMG), but a good option to punish the back of enemy deployment.
This discussion about purity has gone too far, lets be honest here trying to make something easy complicated is not constructive. Purity is determined by the majority of units been the same either by virtue of been the same unit or sharing the same keyword. Otherwise I am waiting to hear the excuse of why a Duo or Haris of Griffin troops in Kestrel Fireteams has a fireteam purity of zero and no fireteam bonuses, same goes with most Duos from units that are not keyworded in both previews.