Why does this make sense? Failing is failing. The only reason it could be true is that the giant corpo has deep projects to pay back for the failure (in theory) but does that work in practice? They've got lawyers for their lawyers and more lawyers for those lawyers. Guess who is going to out lawyer who.
Startups have no reputation. If they fail, you'll be asked why you picked them, and any answer you give is based on your judgment of their abilities, which was wrong since they failed. If you say it was to get X done cheaper, you're the cheapskate who wasted X$ trying to save Y$.
There are also very often situations where your corpo has used corpo X for 5 prior/current projects and is satisfied, so picking them also gives you the backing of those other projects, should something go wrong.
It partially makes sense, but it's also largely office politics. You really don't want to have a complex explanation when you're in the crosshairs of some angry bossman 2 tiers above your boss.