To enroll a child in a school that your friend is teaching in, is phase 2A2, not 2B as per your story so your story does not check out. 2B is Parent volunteer/Church association.
The likelihood of being out-balloted in 2A2 in the pre-merger days is close to zero. Teacher would know who are the other teachers who are also applying for 2A2 since in any primary school the number of teachers that happen to have children that are enrolling in the same year is limited to a small number.
https://tnp.straitstimes.com/news/singapore/how-will-changes-primary-1-registration-affect-my-childQ: WHY DID MOE COMBINE PHASES 2A1 AND 2A2?
A: Priority for alumni members was introduced in Phase 2A1 in 1999 to encourage stronger alumni and community support for schools.
The MOE says it is timely to review the fine differentiation of priority between Phases 2A1 and 2A2 as, over time, more former students and alumni associations have been actively contributing to their schools.
It adds: "The increase in reserved places for Phase 2C will result in fewer places in earlier phases. Several schools may end up with relatively few or no places left for Phase 2A2 registrants if priority between Phase 2A1 and Phase 2A2 registrants continued to be differentiated."
Hence, combining both phases into a simplified Phase 2A would help to preserve access for Phase 2A2 registrants, who might otherwise have no spots left.