I don't care about refuting a theoretical point.

Dissemination of big three alumni into companies, and their use of the services of their former colleagues is a thing I have witnessed, both from the client side, and from the experience from friends at these firms when they left.

It's simply the way these firms work: associates cultivate long-term business/support relations with executives, and they progress in the firm as these relations become more fruitful. It's honestly unsurprising that departing employees are seen as potential clients, and therefore that the firm helps them land as well as they can.