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Thanks for your answers!
http://www.av8n.com/physics/gravity-source.htm is a great gedanken setup.
But the temptations are so so strong:
1) Textbooks (introductory, SR and GR), in my experience, fail to warn against this.
2) Semi-classical quantum mechanics computations (while wrong in the
sense of a consistent theory) seem to be useful; by analogy trying to
do semi-classic computations in relativity is natural.
3) GR is complex, GR computations for actual experiments are scary
and the relation to measurements not easy...