Okay. My thoughts on this.
First of all, I don't really give two craps what any of the writers or producers are saying about. Simply saying it doesn't make it so. It still needs to match with good evidence.
That being said, I think the stardate argument is weak. Throughout Trek, stardates were used to keep time when ships were traveling faster than light. It was not always consistent across the various shows. Therefore, you can't always derive an exact year from the stardate.
There are some things we do know though. There is certainly a point in which the timelines diverged. That was before the Kelvin was destroyed. This means that yes. The Kelvin itself, even though it does not resemble anything we saw in the Prime Timeline, is indeed a Prime starship. Originally.
However, the appearance of the Kelvin is not necessarily the problem. It's really the apprarance of the rest of the ships in the Kelvin timeline. These were very different and a bit more advanced than the ones of the Prime Timeline (let's not forget the Enterprise's big copper deflector disc).
But this was explained by the producers saying the tech was upgraded from pieces of Nero's ship that were recovered in the wreckage of the Kelvin encounter and reverse engineered. Yes I know. I just ranted about producer statements. But these statements fit what we see. We now expect to see more advanced tech in a pre TOS Trek than we would have in classic Kirk era. Keep this in mind because I will refer to it in a minute.
I also think we shoul not just write off visual differences. We are dealing with a visual medium here. The look is part of the storytelling. Sure there will be differences. We should expect it. But the best stories are going to explain it not write it off.
Getting back to it, I believe a case could be made that DSC fits in either timeline but I favor Kelvin. Yes I say that because of visuals. But let me explain it a bit more.
Let me first challenge by saying that if we favor a prime placement, we still need to resolve some problems. In fact at least one major one. That's the Klingons. Sure, they've addressed that no one has seen one in a hundred years. That could be a reference to Archer and Enterprise. But remember season 4 of Enterprise.
For all its faults, Enterprise finally explained why TOS Klingons look different from TNG and beyond Klingons. They had tried to produce Kilngon Augments. It went wrong and Dr Phlox had to use DNA from humans (Archer specifically) to cure the virus. This meant that the entire was subjected to genetic modification and had their appearances altered. But the mod had a shelf life. It would naturally revert in about a hundred years.
Well we saw that happen during Kirk's era. Yes it was actually in the Motion Picture that we first saw TNG era Klingons. What this means for us is simple. If DSC is set in the prime timeline, the Klingons should not have cranial ridges and use Bat'leth-like weapons. This is 10 years before Kirk's era and nearly a hundred after Archer. The Klingons revised look should have been a revision of TOS era Klingons not modern Klingons.
But if this is Kelvin, we have an interesting solution. DSC is dealing with the unification of the Empire. Why? Well we have more modern looking Klingons, and the entire race seems to follow that look. Given that this would take place after Nero has entered this timeline, that would mean things are different to the point where the mod wore off faster. If no one has seen Klingons in nearly a hundred years, that would mean not many saw the missed Klingons that Archer barely dealt with. Not many witnessed the mod so the expectation when these Klingons are encountered would be no surprise. Anyone who did know about it would just assume it had passed by now.
Getting back to tech, DSC does not just feature cool visuals. The tech that is depicted cannot be ignored. DSC uses extensive holography aboard Federation starships. In the ptime timeline, this would not have occurred until TNG era and then only on a holodeck. But holography was known much earlier. Archer and his crew encountered the Xyrillians who used such devices in his era. But still the Fed did not implement any such tech. When Columbia was commissioned and launched, it had no holographic tech.
But if account for Nero and the fleet upgrades from the remains of the ship, such holographic are more than believable in the DSC era.
Sure we still have to explain the uniforms. But I am working on that. I really don't see anything to state that it can't be Kelvin except for actual statements. I find those statements highly questionable at best. Let's not ignore prime timeline problems to blindly accept these statements. We need to see more of DSC and hope we will get some good confirmation.