Just throwing a bit more into the mix.
The "Saudia" aircraft was at FL340 so could actually be anywhere between FL338 and FL342 as ICAO states that an aircraft is at its level as long as it is within 200ft of that level. The GulfAir could therefore also be at FL348 so although there is full level separation between the 2 craft, actually there may only be 600ft.
I'm guessing that the report has typical media poetic license and the figures they state are just a layman's basic description and actual distances weren't released. If the aircraft did start with only 800ft or even the minimum 600ft and a climb was conducted then it wouldn't be too surprising that TCAS got involved.
Be interesting to see what an official report will say - if one is done and released........
