Yeah, it’s pretty true, and the coach should be forthright with the applicant. And they usually are.
Is it a blanket statement? Probably not. There may be some MIT coaches that do have a bit of pull. Even then, it’s nowhere near the level of coaches at that place up Mass Ave or the ones across the river.
The plural of anecdote is not data. 
Without seeing the entire application and being an MIT AO, nobody can say why someone was admitted.