But...this doesn't nip any of the rumors in the bud, actually.
No one, I mean NO ONE was saying Halo would cease to exist. That's crazy talk. The whole thing with the story DLC was probably a reach, but the real meat & potatoes of the rumor, IMO, were the implication of 343i being downscaled to a support & consultation group working with outside teams on future Halo content. 343i would continue with MP, aside from BR.
Also, and this is worth pointing out, realize that they did NOT specifically say 'Halo Infinite', just Halo? As in the franchise/IP? If they really wanted to squash the rumors a lot more, they could have specifically said Halo Infinite, but did not. And this is an official statement.
The way I read it, this is something of a soft affirmation of at least the meat of the rumors, since those were about outside devs making Halo content and 343i acting as technical & lore support (I would assume, as co-developers). Which honestly is still the best option for the IP to be revitalized back to something resembling its prime, put pride aside and do what's best for the franchise.