I would question the statement "Since it’s already rather a common knowledge that programmers are able to solve challenging problems while involved in seemingly unrelated activities", my problem with that is, you may be doing something else, but you are still thinking about the problem, and mulling it over. More to the point, and especially if your program has nothing to do with the company, then designing/writing it while at work is no different then sitting at work figuring out how to beat that last level in starcraft or what not, and planning out your strategies. You could argue that both of them 'improve you as a person', but is the company paying to improve you, or for you to do your job?

Also i would bring up this statement "Programmer is a special type of human breed who do things differently and have a different approach to accomplishing any undertaking. ", this statement just smacks of pointless and unfounded elitism. Theres nothing particurally special about being a programmer, especially when compared to the myriad of other jobs out there. All a programmer is, is a person who can reduce complex instructions into very, very simple commands, and then translate them into whatever language he needs. You may not be even solving problems, but say, rewriting a program in a different language or what not.