Twilio's cost structure is probably dominated by SMS charges from telco operators and customer acquisition, not their AWS bill. So I doubt it, but feel free to cite data that shows I'm wrong. (I read their s-1 and I don't think it got into that granularity of cost accounting)
But they also spend a bundle with AWS... Amazon can reach the same pricing with the telcos, but will have lower infrastructure costs. Twilio would honestly be a good acquisition for AWS, but maybe Bezos feels like doing it himself.
I think it's a market where winning is about customer acquisition and retention, not necessary cost-control, though I'll grant that could become more important over time.
Can we contrast the aggressive Amazon platform vs customer dynamic with other cloud providers?
Why would a new company opt for Amazon at the risk of being copied and competed with as we're seeing with Netflix, Twilio, and numerous Amazon store vendors? Why not go with Google or Microsoft?
Netflix has a lot of customers, IMO because they developed great recommendation IP, they have a large content library, and have invested heavily into customer acquisition and marketing to build a consumer brand.
Netflix will use AWS infrastructure if it benefits their business and go elsewhere if it doesn't. The fact that the two companies compete in some ways is pretty much irrelevant to Netflix's (operational) decision of hosting provider.
You said "considering that Twilio hosts with AWS" as if that's the competitive disadvantage they face vs. Amazon. However, their cost structure would be the same if they hosted on Azure, Google Cloud, Rackspace, or anywhere else. So yes, Amazon may compete on price but I'm not seeing how Twilio being on AWS factors into it given that they need to incur server hosting costs somewhere.