If support is the reason they lost, then the auditors you dealt with were idiots & you should have appealed. A parent may claim EIC even when the kid provides
all her own support. The law is simply not open to interpretation on this.
IRC sec 32: [EIC]
(3) Qualifying child
(A) In general
The term “qualifying child” means a qualifying child of the taxpayer (as defined in section 152 (c), determined
without regard to paragraph (1)(D) thereof and section 152 (e)).
IRC 152(c)(1)(D): [The term “qualifying child” means . . . an individual—] . . .
(D) who has not provided over one-half of such individual’s own support for the calendar year in which the taxable year of the taxpayer begins.
IRC 152(e) is the divorced or separated parents rule that lets the NCP claim the kid as a dependent. This is why the CP gets EIC for the kids rather than the NCP who claimed the kids.