I think you're right about the players, but I also think you're mistaken about tanking being a fiction created by media and fans. At some level there is a decision made to put the team in a position to have less chance of success in the short term, in order for a greater chance of success in the long term. Not every organization does it, but some certainly do.
For example, I followed the 76ers' tankapalooza for several years, and while I saw players giving effort every game, only the blind and deaf could think that organization as a whole was trying to be as successful as possible in each of those years. Will it pay off? The next few years will be interesting.
Another example is the Colts team that was bad enough to land Andrew Luck. Did that organization, top-to-bottom, put them is the best possible position for success that year? I would argue they did not. Funny thing is that while their tactic of tanking succeeded in landing Luck, it hasn't led them to the long-term success they planned. To my way of thinking, the Colts are the cautionary tale about tanking as an organizational strategy.