I would agree with Polar Boy & Chlorophyl Kid. They had the unique super powers & showed they could control them (at least after forming the Subs) Infectious Lass actually seemed to lack control of her power while in the Subs. Once she gained control of them she did gain membership.
Also thought Spider Girl & Radation Roy had the power to get in but maybe they were rejected for being mentally unstable since they did end up in the LSV after being rejected.