Sorry, but I can't accept comparing the price of an apple in 1950 to the price of apple today is not a valid comparison, but comparing the price of a apple today to the price of a horse in 1950 is a valid comparison. There is no list of the price of everything, let alone for every year in history as you imply. Assuming the choices in the items selected for the "basket" are not going to influence the outcome, or that these choices are done impartially seems naive. The goal of the CPI is nothing. It is non sentient and has no goals. The goal of the functionaries who calculate the CPI is to come up with a number that satisfies their bosses, namely politicians. Politicians have only one goal, to maintain or improve their power. The methods used are just way too easily manipulated and the desire to do so too great to expect any result that isn't biased. CPI doesn't really measure inflation anyway. It measures appreciation/depreciation of goods which are based on many factors unrelated to inflation, primarily supply and demand. As it is, I don't consider CPI to an be indicator that can be trusted.
Apples are one of the prices in the basket. Or are you alleging that they were removed to hide inflation at some point?
The BLS compiles the price lists by gathering all (or samples of it, perhaps more accurately) of the data directly from the sources. If you want to be cynical, everything they say is a lie. Having worked for the executive level of government, I'm far less cynical than that. I think some economists at BLS probably treat CPI as their baby, having dreadfully uninteresting discussions about how they might better measure prices in order to make the index more accurate. They're probably professionals, not appointed, so they really don't care about what the appointees want--they'll all be gone in a few years anyway.
I went to a meeting in Washington about dealing with political appointees--how to act ethically, in part. This was a packed room of people from various places throughout the federal government, a retired federal employee acting as motivational speaker. He basically said what I wrote above: I don't want to give in to your demands and I don't have to. I'm difficult to fire and you're terrified to fire me; but you'll be gone any time now--I've seen a lot of you shuffle in and out. Nope.
I think this scenario is constantly playing out in reality because political appointees are always cognizant of the risk that a story could end up on the front page of a newspaper exposing some nefarious manipulation or decision. When you're managing professional staff, it's likely to be your head rolling, and that really must be bounding.
Edit: I feel obligated to take this a step further thinking back on my time in government. If you're a BLS economist, you don't want your shoddy work exposed and condemned by some professor in a journal article. Federal employees really don't act like sheep--they don't just silently follow whatever commands are given by superiors. With respect to professional staff in the government, whether they're engineers, economists, lawyers, or whatever else, these often aren't incompetent people who are hopelessly dependent on that federal job. A multitude of professional staff works for the federal government because that's what they sincerely want to do with their careers--work for the public. I can think of many people I knew who could have easily made several times their salaries in the private sector, if that's where they found themselves. That kind of person doesn't just roll over and follow orders: they immediately think of their personal mission, their ethics, and their professional reputation when they're asked to partake in murky behavior, and they stand up, arguing for the right thing because they really have nothing to lose. I think they win far more battles than they lose, and that makes the information supplied by professional staff quite good.