Many Singularitarians assume a lot, not the least of which is that intelligence is fundamentally a computational process.
What else it would be? Except the divine origin of thoughts nothing was submitted as an alternative so far.
Building an AI does not require it being a computer - it could be a bunch of rubber bands if that's what worked. The assumption is more like intelligence is not inherently mysterious, and humans are not at some special perfect point of intelligence.
http://opinionator.blogs.nytimes.com/2011/12/25/the-future-of-moral-machines/