I don't disagree that having a big name on resume can be helpful. But I do think there are other things that should come into consideration.
I worked at several no name startups right out of college. And yes they failed, but I was also given huge opportunities and responsibilities that I never would have had at a larger firm.
And as a hiring manager I don't let names on resumes be my only driver. Just because you worked at Amazon straight out of college doesn't mean you are amazing. It just means they gave you a chance. And it doesn't mean you've done much, you may have just been stuck fixing bugs on one very small aspect of one system. That isn't very valuable in my eyes.
So I think it's worthwhile noting that there is a risk at startups and the name recognition is definitely useful in a crowded market. But name recognition will only get your foot in the door. You'll need some real experience to go the rest of the way, and I have nothing but my years at failed startup to thank for that.