Whilst I would imagine that to be the case, you should at the start of a phd have more than one professor across the many you have come into contact with that is willing to vouch for both your mathematical ability and your personality and ability to fit in a team.

I don't think anyone should get in just on the relation to Tao, likewise it is also important that they move to a program that they have an interest in.

I do hope those students find an appropriate course for themselves as this must be extremely challenging for them both regarding their career and also mentally and socially.