Interesting stuff this. I'm just thinking about a few possibilities here. One is, if the application requires the level of precision we are talking about here then why would you choose to use black bar or similar, which is bound to be far from perfect? I assume we are talking about long lengths here. Second, a very short piece of square bar is highly unlikely to be bent by any significant amount.
Thirdly, there is no reason to suppose that a piece of round bar of similar length and quality to the square stuff we are talking about wouldn't be bent either.