Thanks everyone for your input! Just to add to the discussion, I showed the pictures to 2 people in my local birding group and here is their conclusion:
"We think that the shorebird that was displaced by the Peregrine Falcon is a Ruddy Turnstone based on the following field marks:
*The tips of the primaries and the secondaries are black
*The base of the primaries and secondaries are white
*The primary coverts are black and the secondary coverts are brown
*There is an alternating rufous/brown, black and white pattern that is unique to the Ruddy Turnstone
*The body is stocky
*The underbody is white with a dark breast band.
*The base of the tail is white with a subterminal black band on the end of it.
*Compare the tail of a Black-bellied Plover and you will see the difference.
*There is black in the head
* It has a chisel-shaped bill