In one word: reputation. These schools want to be seen as social-responsibility leaders, etc. I don't want to sound so negative about it, but there's some element of publicity these institutions are seeking.

Think of this: how many people criticized Steve Jobs for not getting involved in charity, although he had billions in the bank? Do you think it looks good for Harvard University, with over $15bn in endowment to not do any good will project?

Lastly, some of these schools already offer remote learning via video. Putting the videos on iTunes is a sunk cost.

Disclosure: I went to one of those "big name" institutions as an undergrad, grad student, and I also worked there. Few are the projects that are TRULY out of the goodness of somebody's heart

You said "Other institutions in the 'diploma business' will surely peek and try to keep up and I do not see or understand the benefit for Harvard, Stanford et al. if we are not talking altruistic purposes."

My response was on the point of whether other institutions in the "diploma business" would peek to keep up. I was merely stating why Harvard, Stanford, MIT and the like have nothing to fear by opening their courseware. My intentions were merely to diffuse the notion that replicating instruction would suffice to compete with Harvard.

As to why they do it, I think other comments have covered that.