Burry's point is not that a lot of indexed stocks are relatively illiquid and thus index funds would have a hard time getting out of them in a serious downturn.

His point is that the index funds don't own the stocks at all; they trade derivatives like futures and CDO's that mimic the movement of the stocks in leveraged fashion, and the more people who dump their money into index funds without doing their own research, the more leveraged the funds become.

He's warning that in the next serious downturn, over-leverage may cause cascading collapse of index funds and the economy with them, like it did in the mortgage finance crisis.