Dave's PointInTimeNowObject describes itself as:

  I am based on the naive assumptions that time can be represented as
  a single continuum which may be experienced identically at different
  physical locations and velocities, and such that two observers in
  two different locations can identify a single PointInTime as a
  simultaneous event. These assumptions are not valid when relativity
  is taken into account, but are acceptable for use in Newtonian
  physics and Smalltalk.

I think it isn't really as bad as that. Time is experienced
differently by different observers. However, UTC includes for free, no
extra cost, its own preferred reference frame. Using this frame, two
observers may identify a single PointInTime as a simultaneous (in that
frame) event. Of course, if I am in a significantly different
reference frame, then I will experience local seconds at a different
rate than UTC seconds. But as long as everyone uses the same frame to
communicate, that is, so long as Dave's methods all refer to time in
UTC, then there is no ambiguity.

There are relativistic problems with UTC seconds, but I think these
are problems of complexity, not ambiguity. The relation between the
rate atomic clocks run on the surface of the spinning, non-spherical
earth in its non-circular orbit around the sun and the rate clocks
would run in simpler reference frames is messy. A somewhat telegraphic
discussion of the complexities is available in section B6 of
http://maia.usno.navy.mil/iauc19/iaures.html

-- 
Stan