I don't think that you own a digital ocean or ec2 instance - you rent them the same way you are renting the service this thread talking about. Given that chrismonsanto, is taking an even more hard line approach to controlling his stack than I do, I'm assuming he agrees (I know - dangerous).
When I talk about my servers I'm talking about things sitting in my racks (possibly in my server room), that I can rip components out of and upgrade. I'm talking about very expensive things, if not in terms of purchase price, certainly in terms of care and maintenance.
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And to tie it back up to my other comment, I think there is value in owning your own servers, and in coding your stack from top to bottom, and having no external dependencies. But I think these are both very expensive choices - and the kinds of choices, most startups don't have the time/money for.