This. So many founders are enamored with their titles and their ideas more than actually building a real company. IMHO its the most obvious way to spot a future failure along with the amount of fluff PR and "thought leading" blogging...
CEO. The product owner should be finding what the customer needs, but as soon as you have more than one customer you'll have antagonistic pressures on what to implement next. It's up to the CEO to make the decision which customer needs to actually fulfil (with information and input from everyone else). It's up to the CTO to make those decisions happen in a way that doesn't stop the company doing more things in the future.
CMO. It's the result of the first decision the CMO makes (market strategy).
In short - CMO, CEO, COO AND CFO set the overarching strategic objectives (2 or 3 generally), then that gets turned into a framework for strategy and decision making to enable actions to be evaluated, enacted and measured.
At the highest level, the framework consists of:
1. Strategic aspirations - what are you aiming to do, and how will you judge the success or failure of those things? Goals, KPIs and success/failure criteria.
2. Where to compete (product category areas, pricing, distribution methods, experiential factors, communications and branding)
3. How to win - what will preferentially differentiate the offering, and how will it be distinctive against the market competitors.
4. Capabilities audit - what needs to be changed about what the organisation has/does in order to enable that, and how will the effects of that play out throughout the rest of the organisation?
5. Change management - how are those things going to be introduced/amended/reduced/removed and where does the responsibility lay for those changes?
Everything the organisation does should be in support of the strategic objectives, and thought about in relation to that framework.
As a result, the product-market fit comes as a result of product decisions, and how's it's positioned to the market is a result of the decisions for 2 and 3.
Note that product-market fit isn't just about what the product does, but how what it does is communicated to the market. Both of those are vitally important, bit people tend to forget the comms part.
If the org isn't big enough to have a CMO yet, then generally it devolves to the CEO.
It's why start-ups tend to have crappy product-market fit - CEOs tend not to be great at understanding marketing.
CEO is the primary but everyone in a startup needs to take responsibility for this. The core goal of a startup is to discover a "scalable and repeatable" business model.