I will say that a CTO of a large company has to have a really good read on the technical constraints. Whether this is achieved through technical expertise, or having a warchest of talented lieutenants is an implementation detail. That said, even the lieutenants can't be in every room, and if the company faces substantial technical challenges, there is a high risk that a non-technical CTO makes commitments the team can't live up to.
In a well-functioning team, a lot of this can be papered over by the lower-level folks (managers and ICs) finding a way to do the right thing on an unofficial basis. I would go so far as to say that all successful companies depend on that unofficial network of clueful employees doing the right thing in spite of formal guidance. But at some point leadership is going to have to make some decisions, and when that time comes you better hope they have put at least as many hours into their relative domain competence as they have into schmoozing big wigs.
Technical people looking up from the bottom often expect some type of meritocracy where being good at your job earns you promotions and responsibility, but that isn't really how leadership works. When you are trusted, you get promotions. For exactly the reasons stated above - leaders delegate to people they have worked with before and trust that the needs will be met.
So as a leader, decide who you trust. As someone lower down the chain, work to build that trust.
If you're a CTO, do you trust your person A or B? If you're not technical what do you base it on? What are you judging?
Are you judging based on their personality? The number of brownbag talks? The feedback from peers?
What you want is for someone to know how things work. And if they don't know, know what to ask. You want someone who's done it before. They have to be technical.
You want your chief of plumbing to know how to plumb. You don't want them to just be familiar with plumbing. If so, the next thing you know a good salesperson will talk them into replacing all the pipes with new wonder-pipes with space-age wonder-clamps.