It's not obvious why you consider it arrogant so may be you should explain.
I personally think it is a good idea and keeps things simple. Combining them together probably requires more coordination and thought for the product--and at the end complicating it.
You can make this argument about any nice domain name. Does Facebook Inc have tacit ownership of the concept "facebook" (collection of photographs of people, in case you've forgotten the real meaning)? How is this greatly different?
Domains for large organisations are exceedingly complex webs of power and politics in most cases. Stanford is pretty big in an organisational sense (I don't really know, I am just assuming based on the amount of money they have in the bank). I wouldn't be surprised if they are using generic domains because it is easier than trying to get other departments, powerbrokers and administrations to all agree on something.
While I disagree with the arrogant label, I do wish that a standard class.stanford.edu or stanford.edu/class template was used. (Not to leave the domains open for others, but to prevent confusion later when the space gets more crowded, as I suspect it will.)
Arrogant how? I have no college education and I am currently developing a health application so I am extremely excited to have the opportunity to take these courses. There is nothing arrogant about this and not only do I applaud them for being the first school to do this but I hope that other schools ie: MIT etc... follow suit.
> I hope that other schools ie: MIT etc... follow suit.
Which is kind of his point - they will have to choose a domain that is either also generic (anatomy-course.org), which would be confusing, or use something like (mit-class.edu/anatomy) which is less memorable.
I wouldn't go as far as calling stanford arrogant though - they came first, everybody had the opportunity to do this for a decade.
MIT has been doing it for a decade, except for the coordinated enrollment (study groups) and automatically graded exercises (both of which are nice enhancements, but the ML class exercises are mostly pointless.) http://ocw.mit.edu/