> Not under any definition of public transit I've heard

From source [3], as provided above:

>> The taxi should not be viewed as antagonistic to public transport, people who use taxis are in general 'public transport users' not 'car users'. Any improvement in the taxi service should therefore be viewed as an important improvement in public transport provision. Any improvement in the provision of taxi services will be very valuable for people with mobility problems since they rely on the taxi for a significant amount of their travel due to the door to door nature of the taxi service.

> They cause congestion proportional to their users, i.e. orders of magnitude more congesting than buses.

As other comments have discussed, this is controversial.

[0] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2838043

[1] http://www.schallerconsult.com/rideservices/automobility.pdf

You're begging the question—you didn't quote a justification for the term, you quoted an argument that requires the same justification.

Taxis are absolutely antagonistic to public transit, as demonstrated by the ratio of human labor to humans transported. Cars are simply the most comfortable version of transit available to people who have the means. It is not available to those without the means. The idea that the taxi users are the same as bus users is simply being class-blind.

Public transportation isn't about who owns it, but who has access to it.

That's a hell of a claim to back up. Any kind of argument for this idea? Ownership is meaningful. What is access—is my local McDonalds a public service?

This smells very similar to "access to affordable" housing and healthcare. Sounds great, but at the end of the day, people are still without health care and housing, so they clearly DON'T have access. Ownership is the only way to guarantee material access.

Will you be satisfied by a dictionary definition:

  buses, trains, subways, and other forms of transportation
  that charge set fares, run on fixed routes, and are
  available to the public.

I will agree, many taxi services are (in practice if not in principle) excluded by this definition. Discriminatory practices with how they select their fares, for instance. Also most don't have fixed routes so you'd have to relax that requirement to allow taxis (but some taxi shuttle services operate on more or less fixed routes).

I still don't see that as a materially useful definition but I'll admit I recognize the usage.

However, in the current context of discussing congestion—i.e. who gets to use the thing we all pay for—and other externalities like pollution and use of fossil fuels, public ownership is the salient thing to discuss.