Pepper is a very wise lady.
I doubt anyone will argue that water is the best choice of drink to have...regardless of whether you're trying to lose weight...nature beats manufacturer any day of the week.
But these "studies" don't really prove anything. When reading such "studies" ALWAYS ALWAYS ALWAYS ask yourself questions like
"who funded this research"?
"have they got a hidden agenda...something they need to sell for example?"
"what are they REALLY saying when you unpack all the media spin?"
The first article that was posted basically said nothing ... it didn't say diet soft drink causes obesity (in fact it made it clear there is no causal link) and it did say that there were too many other unknown factors to have any idea why 40% of the people in their study who drank diet soft drink became obese. Pointless frigging article if you want my opinion (I know you didn't ask for it but I am quite passionate on the subject of bogus so-called reporting on science).
The second article that was posted has zero credibility because the guy was selling nutritional supplements. His "facts" are going to support whatever line he needs you to believe in order to buy his supplements.
So...if you want to drink a diet coke (or coke zero or whatever the heck else you like) after you've had your 2 litres of water...go right ahead...if you're eating right and doing your exercise it is not going to have any detrimental impact on your weight loss whatsoever.
Except maybe If you drink a lot of caffeinated diet soft drink you'll have trouble sleeping and may get too tired to exercise but that's about the extent of it.
There isn't a single study out there with any proven scientific fact in it that proves otherwise. I don't count paid advertisements or "news" articles masquerading as such by folks with something to sell.
I'm climbing off my soapbox now.