So, we re told to bow perpendicular to the strings. Straight across between bridge and fingerboard. 

I get that the midway between the fingerboard and bridge is relative as to what you are doing. On cello we play closer to,the fingerboard to get a softer sound. So, I don't say anything when I notice someone playing closer to the bridge or closer to the fingerboard, at least with cello, I was told that sometimes you don't for affect.

But, the statement about going straight across seems to be a "do what I say, not what I do". I have watched professionals and they do not bow straight across. They are bowing at an angle. It is most obvious to me with cellists. They have the bow angle to the floor, not across the strings. I have seen it with violists and violinists, bit not angled to the floor, but not straight across. I was told that that is what causes the grainy sound.

This has boggled my mind for a while. I pay attention and try to bow straight across, but what I see with those who are more in the know, they do not practice what they say. It seems very strange to me.

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