To defend my post, mixpanel is providing copy/paste html with a link for people to put into their footer in exchange for services of monetary value.

Could someone explain why this does not qualify as an ad?

On Google's published guidelines and guidance, this is white hat, as the links are editorially chosen (you, the webmaster, really are specifically intending to endorse them for their analytics services because you use their analytics services).

The shadow rule is that any linkbuilding method is kosher iff no one has figured out a way to scalably achieve rankings on very competitive terms with it. For example, citations on the footers of blog templates were 150% A-OK right until people found out that was a scalable way to rank e.g. for e.g. [printer cartridges], [payday loans], etc etc. See also widgetbait, quizzes, etc etc.