At work, I'm not allowed to install arbitrary software as well - but policy doesn't make my workstation any less of a computer. Also, not all smartphone vendors are as anal as Apple, and there are always workarounds [1],[2].

I don't think we actually disagree - it's just a matter of definition; please note that I intentionally didn't say (personal) computer, but (general-purpose) computing device.

[1] http://en.wikipedia.org/wiki/Rooting_%28Android_OS%29

[2] http://en.wikipedia.org/wiki/IOS_jailbreaking