There's a group at the University of Alberta that does research in poker strategy. They have a program that plays heads-up poker (2 players) as well as the best in the world. Adding more players into the mix significantly complicates things though, so it will be a little while yet.
There are people that run bots on online poker sites, to varying degrees of success.
Note that the person you are replying to specified No-Limit, which is much harder. It's been a while but last I looked the Alberta Group could only do Limit Poker.
Those bots have gotten significantly better the last few years. I would say the best bots today are beating nearly all of the recreational players and even the lower rungs of professional players - but the very best players can still beat them, should they be paying attention to their tendencies. The bots have a big advantage over them though in that they are robots: they don't get tired or hungry and their judgment never gets clouded on runs of bad luck.
PokerStars and FullTilt have worked hard to rid their sites of bots but many other networks have turned a blind eye to them, some even explicitly allowing them - since the bots pay rake like any other player. Every so often the players will revolt and the sites will crack down but the bots always find their way back again.
I agree with everything you have said, but it is worth pointing out that the best online players are assisted by bots. The top players use software that can immediately show your last 10 bets and the outcomes as soon as you raise.
My point is that if you play low stakes, you get crushed by patient bots. If you play high stakes, you get crushed by cyborgs.
Im not positive that the current HUDs do that , and even if they did, i dont think its a huge advantage. Players use statistical tools which could be seen as unfair , except they are so common now that a significant percent of players from the lowest stakes to the highest use these tools. Just having this data is not enough to make soemebody a winning player as it does not suggest a specific move, the player still needs to figure that out. High stakes players are just much, much better than lower stakes players, with or without the HUD.
Those tools present their own problems but they aren't bots. Bots are making decisions and acting on them, not simply providing additional information for players to incorporate into their decisions.
There are people that run bots on online poker sites, to varying degrees of success.