Let me give it a try, the "Froome dopes" story. Probably forgot plenty of things but it could be a start:
1. As a young rider, Froome showed talent to become a decent pro. He has results that put him among riders such as Cyril Gautier and Andrey Zeits. Early results as a pro confirm this, however he went backwards until suddenly bursting out at the Vuelta 2011 and become the dominant GC rider of his generation. Winning another Tour would put him at 3, something less than 10 riders have accomplished in the history of the Tour. Adding a 2nd place in 2012 and two 2nd places in the Vuelta makes him one of the better GT riders ever in a timespan of just five years. Nothing he ever did prior to the Vuelta 2011 suggested this was even remotely possible. It is hard to find other riders with a similar increase in performance. The most similar appears to be Riis, widely known as an ultra-doper. It is also hard to explain this performance increase.
2a. Bilharzia is most often cited as the cause of Froome underachieving, and curing this disease caused the performance increase. In other words, the disease makes the difference between a multiple Tour winner and someone who may never win a race of any importance. It is thus an important chapter in Froome's life. However, both Froome and Sky have told multiple, conflicting stories about when and how it was discovered that he had the disease, and how long he might have had it. Moreover, it is hard to imagine that it took so long for them to notice that a) something was wrong with Froome and b) find out it was Bilharzia, a very common disease in Kenya that Froome's brother apparently suffered from. If your potential Tour winner gets dropped from the grupetto in the Giro, clearly something is wrong. Took them a year and a half to sort it out?
2b. Froome and Sky's stories about the effects and treatment of Bilharzia are sketchy at best, hard to believe or plain wrong according to people who know about Bilharzia. I am not one of those people so I won't discuss it further.
2c. Bilharzia doesn't explain why Froome did not show multiple Tour winning potential in the years before the disease.
3. Another possible explanation for Froome's rise is that Team Sky is just that good. The famous marginal gains. They are touted proudly as the reason why Sky is able to beat the evil dopers. It is a term they launched without anyone asking them to, they did it as an argument why they are clean. However, until this day, they have not told of anything they do which a) is useful and b) is not done by at least some other teams. Some examples given are easily debunked: pineapple-flavored water has been used for 40 years; and there is an actual image of a Sky vehicle containing a pallet of Nutella "because the riders like it so much".
4. There is also the "Sky has so much money, they just buy the best riders" story. This was definitely not true at first: from their Tour-dominating squad in 2012, only Boasson Hagen was one of the best riders in the world before going to Sky. Froome, Wiggins, Porte and Rogers improved (a lot) at Sky. Knees and Sivtsov were nothing special.
5. Froome improved by losing a lot of weight. This does not explain how both his climbing and time trialling improved dramatically. After losing part of that weight in his Barloworld days, Froome did not exhibit noticeable improvement. Somehow his improvements due to weight loss came suddenly between the Tour of Poland and the Vuelta in 2011.
6. Sky was unaware of what Froome was capable off even during the 2011 Vuelta. He would have won that Tour if the team wouldn't have sacrificed him for Wiggins. They did so because they didn't think he could perform for three weeks. Surely they would have given him a free role if they had known that he was a potential multiple Tour winner. There is also that annoying "estimation of Brailsford's rider analysis" graph which has Froome as the least talented rider on the team in 2010. Turns out he was by far the most talented. Small mistake.
7. Froome has no discernable skills as a cyclist apart from raw power. Not good at handling a bike, not aerodynamic at all, and his only tactic is to ride fast and drop everybody from his wheel.
*** So, Froome improved dramatically without a reason. Why would the reason be doping? ***
1. Geert Leinders worked at Sky and is banned for life for doping practices
2. Sky wanted to be a clean team from the start, not having anything to do with doping. They hired Leinders, de Jongh, Rogers, Julich, Cioni, Barry, people who were pretty much known dopers. Froome worked a lot with Julich, who apparently did not dope at CSC ... Okay, so Sky doesn't actually mind working with dopers. Just PR.
3. Sky hired a bunch of riders scoring high on the UCI's 2010 suspicion list
4. Chris Froome hacked his way into a championship as a young rider. He also hung on to a car, got an energy gel when it wasn't allowed, and got a backdated TUE. And as the saying goes, “If I’m a liar and a cheat and if my ethics and morals are all about cheating, then surely I’ll be doing it in other places in my life. Not just parts. If you’re a cheat, you’re a cheat, you’re not half a cheat. You wouldn’t say, ‘I’ll cheat here but I’m not going to cheat over there. I’ll cheat on a Monday but not on a Tuesday’." Or, as the saying also goes, "If you want something bad enough, you'll find a way to get it". Those are Brailsford and Froome quotes.
5. Performances bordering on the "limits of human physiology" and occasionally up there with the best from the Armstrong era.