First of all, they are not saying there is one true metric that rules them all. They said each site will have one key metric, which makes a lot of sense. Each site will most want to measure how users engage with their domain. The example mixpanel offers is that Instagram wants to know how many users uploaded a photo. This matters way more than pageviews, etc. It tells you something about user engagement.
The bigger issue I see in your comment is that sites at different stages in their lifecycle will want to measure different things. Customer lifetime value is the most important number for a mature business but early stage startups are nowhere near getting a realistic number for customer lifetime value. If I am the founder of a startup I want detailed knowledge of how users are interacting with the product I created to address a problem domain. I can get that info immediately after I start acquiring users, well before I have an idea of whether I have a viable business and what my customer lifetime value is going to be.
It seems to me, if Instagram could really only chose one metric to track it would be an app visit, not a photo upload. Instagram must have users who are primarily content creators and another larger group (probably a superset) that are content consumers. Not focusing on the actions of the content consumers would seem really bad for business since what early-stage Instagram's investors care about is eyeballs not photographs and what late-stage Instagram's advertisers care about is eyeballs not photographs.
Really Instagram probably has a few OKMs (visits, uploads, hearts, comments, follows). All of those are important and should be tracked. In their documentation and educational videos, I've not seen Mixpanel focus on visits as a key metric. I'm not sure why.
The bigger issue I see in your comment is that sites at different stages in their lifecycle will want to measure different things. Customer lifetime value is the most important number for a mature business but early stage startups are nowhere near getting a realistic number for customer lifetime value. If I am the founder of a startup I want detailed knowledge of how users are interacting with the product I created to address a problem domain. I can get that info immediately after I start acquiring users, well before I have an idea of whether I have a viable business and what my customer lifetime value is going to be.