The ISRG contains members from U Mich, Stanford, Mozilla, Akamai, Cisco, and several others. Their top level CA is signed by IdenTrust, who I could pay if we had to. That's really my biggest question on the whole thing ... how did they convince Identrust to add their authority to LetsEncrypt when it's really a competitor to their product?
But practically, when the management is talking fried chicken instead of steak for the Christmas party this year, it seems a good idea to cut costs. I'm covering six or seven subdomains with one cert, which is very pricey when you pay Comodo/Verisign/GoDaddy, etc.
As for being a "black box", the docs pretty much say what they do, and I have checked most of the files they create, and I've read some of their code.
Sure, they could install a backdoor if they wanted to. But for that matter, so could the Apache Foundation, the nginx people, MySQL (which is owned by Oracle now, so, big bad corporate types have software on my F/OSS servers --- hello to the NSA?), and so could Zend themselves, for that matter (hello also Mossad, which might be scarier than the US types).
Part of the F/OSS principle is that peer review, and being exposed for review, will keep vendors on the "up & up". And in the end, it's not even so much that I trust the cert authority; more importantly, are our users trusting us? That green lock on 7 sites for free? We decided we were able to take the risk.