It does seem like he was intentionally or unintentionally building a universe where it was the "internal team" who developed it, but frankly I'm not sure that's a big enough misstep to warrant the marketing company replying like that trying to "out" him. In my eyes, that's an extremely unprofessional move on their part.
We bring in outside engineering contractors all the time to work on stuff. When the feature is finished, we don't tell customers "thank you, yes we're very happy with the work our engineering team and McKinsely & Sons Contracting Firm LLC did for us". That just straight up never, never, never happens; we take responsibility for both the success and failures of our contractors. Of course, success is always nice, and when directly asked we don't hide it (on the contrary; we're happy to give them some free word-of-mouth marketing if they've done good work). There's an alternate reality here where the marketing firm maybe reaches out privately and says "hey Brian; your tweets really paint a picture that we had nothing to do with it; mind giving us a shout-out?"
But that's not the direction they went, and instead they just aired dirty laundry in a public forum. Actually, its not even dirty laundry?! Its just laundry. I can say with absolute certainty that if any contractors/third parties pulled this stunt with us, we'd never use them again, period. Beyond anything else, NDAs are SOP in exchanges like this, I'd bet my life savings she absentmindedly signed one; to throw out a tweet like that isn't just unprofessional, its potentially litigable.