User blog comment:Master Plaga/Something I thought of/@comment-3517267-20130713195617

Well, Rei is to Lilith what Kaworu is to Adam. The Eva-01 is made from Lilith, so technically speaking it's not a problem for her to pilot it as they "share" the same body.

And if I remember correctly, Rei pilots it only in the manga and only one time. And that time, she did pretty bad in her fight. I suspect a bad rate of synchro with the Eva-01.

Also, one could speculate that Yui wasn't fully "awoken" as the Eva-01 and that the latter was more of a puppet than a fully-sentient living being at the time. This could have let Rei pilot it.