Agree about Burnham's Marxist background showing throughout his analysis and predictions, and tend to find it inadequate in many respects, but he would likely reply that the so-called alliance is a temporary stage in the transition to managerialism and that the alliance is better understood as individual capitalist finding positions within the new managerial ruling class and becoming managers along the same lines as feudal lord's becoming capitalists during the previous social revolution. (Not sure if that is the meaning of your "manager-as-owner" designation.)
It seems clearer when one looks at the CCP where the capitalists are clearly subordinate to the manager class. Or in Soviet Russia where the managers eliminated the capitalists and to control over the distribution of productive wealth. (In contemporary oligarchic Russia there was a seeming inversion of the process post-USSR but I understand those positions as being subordinate to the state. Something like "serving at the pleasure of the state". And of course in Nazi Germany there was an apparent alliance of the big capitalists thinking they would have better luck controlling Hitler than the revolutionary labor movements.
I understand managerialism to be rule by those who have (or are thought to have) the skill to coordinate the productive capacities complex modern vertically and horizontally integrated economies at scale. TARP was a good example. The Global Pandemic Response is another. It is the updated, digitally enabled, realization of the dreams of Technocracy, as articulated by that early 20th century dream if globally coordinated, centrally planned, supranational managerialism.