[OBR] Rule 5.06(b)(4)(G) for those who want to look it up.
If all runners, including the batter-runner, have advanced at least
one base when an infielder makes a wild throw on the first play
after the pitch, the award shall be governed by the position of
the runners when the wild throw was made.
Interesting. I wonder why baseball has the time of pitch designation then when really everything is time of throw.