I’m pretty sure that’s exactly what he did.
We learn in the Prologue to ACOK that only half the Stormlords actually sent men to Renly, while the other half “sit behind their walls waiting to see how the wind rises and who is likely triumph.” And Selwyn Tarth is explicitly listed as belonging to that faction, as Davos reports:
“I broke bread with Gulian Swann and old Penrose, and the Tarths consented to a midnight meeting in a grove.”
So yeah, I think Selwyn held back his levies but let his idealistic daughter pursue her dreams.