As you describe the play, yes, it is the PU responsibility to make the call at 3rd; as long as the throw went directly to 3rd, that is. The "holding zone" part way up the line is to allow the PU to read which might be the initial play. If the throw appeared to be to home first, then the throw (back) to 3rd would be the BU, as well as responsibility for the BR. This is the mechanic that should be used; too often the PU stays camped behind the plate with no play, and the call at 3rd is made by a BU trailing the play, without a good angle for that tag play.
And, for the most part, the timing decision also belongs to the PU. In this case, it wouldn't be inappropriate at all for him to confer with his BU for help from that potentially better angle, but that call also is made by the PU. While his angle may be perceived as difficult, one might assume he had a very strong belief of that timing to wave off the run. Given his knowledge and performance in coming up to take that (most often) missed mechanic, I would be tempted to give him the benefit of doubt in this case. (JMO)