A little research would seem to indicate that DME did in fact have it's origins from south of the equator. Now whether this is the same DME that later appeared in the US markets via Collins Radio/Bendix or others remains unclear to me.
I believe DME was mandated by the FAA after a United airlines DC8 overran a holding fix and then had a mid air with a TWA Constellation over New York. A deadly crash with the DC8 falling on the city. After that accident, DME became a required avionics addition.....at least that's how I recall it.
