Everyone I know tightens the turnbuckle with a screwdriver. Why a wrench/spanner?
I'll keep it simple...
That type of turnbuckles are designed to support tension forces only, and has very little torsion strenght, mainly because there are very little lateral efforts they need to support.....it's made that way when the turnbuckle is made, when the metalurgists make sure the grain of metal is more oblong, making it tension resistant, harder, but less resistant to lateral forces.
In using a screw driver, you are stressing the legs of the turnbuckle with lateral forces, (for which the piece was not designed for), and even twisting the turnbuckle legs, wich then get stressed, and the integrety of the intergranular structure gets compromised, possible causing it to fail at a later stage.
For this reason, the turnbuckle manufacturers make 2 flat surfaces, like a nut, to use a wrench, that will in turn provide rotational forces without stressing the legs of the turnbuckle.
Hope it was simple.