Wow,
Keepitreal and I are on the same page here. You should also check out the one I linked - it is what most people consider to be Bjorling’s best - a 1944 radio broadcast.
Still, the 1960 recording Keepitreal linked, made the year Bjorling died, is a marvel to hear as well. With Birgit Nilsson as Turandot and Renate Tebaldi as Lui, in addition to Bjorling’s Calaf, it is my favorite recording of the complete opera.
True or not, it's a major-goosebump story...