The parameters that TCAS utilise are not able to be modified by the crews, and are "factory set",
lame.
Depending on the type of transponder that the lighties are using (whether or not it incorporates altitude reporting), may cause the crew of the other aircraft interrogating the lighties Tx (in this case
VB) to receive a warning. If the lightie does not have Alt reporting on its Tx, and it comes within a specified range, then TCAS assumes that both aircraft are at the same altitude (when in fact they might be separated by a 1,000' or more).
If the other aircraft does have Alt reporting, then rate of closure is incorporated into TCAS' calculations, and advisories are issued to both aircraft.
So although the ATC'er may have been aware that both aircraft had sufficient vertical separation, TCAS
may have issued a command to the
VB crew - which is an aural warning, and REQUIRES the crew to disconnect the autopilot, if engaged, and follow the TCAS command, regardless of ATC instructions.
Hope that clarifies things a little.