My training score doesn’t appear to be moving from runs (not that there’s enough of them to influence it) but I’m now up to Zwift Running level 2 (and 1/3 to level 3) after a couple jogs this month. Appears they’re piece-meal implementing outside running into Zwift stats but it’s still in progress.
They have sorted it out, my training score is back to 0,7 (yesterday it was 22) 
So it was false alarm - running doesn‘t count towards training score.