They didn't add H1 multiplayer because as Frankie said the experience wouldn't have been good because of the latency, but now that there's dedicated servers for the Xbox one that's no longer an issue for H1 so they could do it.
Dedicated servers won't magically solve the "Halo 1 wasn't built to be played online" problem, which was always at the core of Frankie's excuses. Halo PC ran on dedicated servers and it had quite a bit of latency. Even if they were to rebuild some parts of Halo 1's networking (or lack thereof) to curb some of that latency, they're still going to end up with something that "doesn't feel exactly the same as it did on the original Xbox", which was the line that Frankie repeated over and over again.
The fragmenting the player base reason was just an excuse. Besides, if they put them all on one disc are they really fragmenting the player base now?
I don't know -- you'd have to ask Frankie where he draws the lines in the playerbase fragmentation. The "fraction of a fraction" of the Halo playerbase that would have been playing an online-enabled Halo 1 multiplayer with Halo Anniversary was apparently significant enough to avoid that potential fragmentation, and this rumored collection would technically be splitting the playerbase four ways. Either way, this whole thing is bullshit and if this cumpilation includes the thing that 343 said couldn't happen, then I feel like that's a golden ticket to the outrage-factory. I will be vociferating this hypocrisy until I'm on my deathbed.