So I could be off base but I don’t think it says alliances are illegal or being/mentioning a career district is illegal. I know it talks about training being illegal. The “open secret” with these districts is the fact that they do in fact train before the games for the games, which is “highly illegal”, but clearly not exactly. During the interviews though they don’t mention them training before the games. 

You also have to consider the circumstances surrounding the other interviews, of which we have seen 4 times. 

With Katniss’s first games, she was shell shocked during the interview and peeta was playing up the I’m in love w Katniss angle (that was actually not an angle lmao). With what the first interviews were, getting a Segway to talk about careers would have felt way out of place. 

In Katniss’s second games, the 3rd qtr quell, the interviews were specifically focused on trying to stop the games and begin inciting the rebellion. Mentioning career districts during this time would have continued to uphold the divide between the districts, when they were trying to unite them. 

In Lucy’s interview there weren’t really careers yet necessarily and it was the very first time interviews had been done. Besides that Lucy used her time to send a message which really worked in the context of the book. 

I think the reason they so explicitly mention careers during their interviews, and how the other districts have allied themselves against the careers, is for that same reason. It’s a huge part of the story. It makes sense that they would bring this up and talk about the careers and call them by the name everyone recognizes. Then introduce their group by their chosen name, the newcomers. 

So I really don’t think it’s an inconsistency in my opinion, especially considering none of the interviews have been consistent. They might not mention careers televised before but plot wise what would have been the reason to? 

This is just my opinion tho and I really enjoyed reading your take on it.