Well, that's not what HTML, nor the underlying HTTP, was designed for. I don't see it as being an appropriate platform for software at all. (And I don't see plugins such as Flash as being the solution either. I believe this needs a completely different protocol, e.g. NX is something going in that direction.)
As always Kevin I agree with you. These people don't understand basic OSI network layers; rather obvious textbook stuff.
And IMHO, as a Free Software distribution, we should do all we can to promote Free Software installed on the end user's machine where he/she has full control (freedom!) over the software rather than remote services, web or otherwise.
If we tolerate any non free software then what's the point? Why not just run Windows or OSX?