Marching Ants Emulate Edge of Selection - Rectangular Marquee Tool

Perhaps I need to ask a different question. If what I wish to do is fill in the section circled in red (pictured below) with the paint brush or clone stamp and I need to ensure that the paint is contained and the edge that it creates is perfectly straight, what is the best way to do it? Thanks in advance for any and all suggestions.

When I initially make the rectangle they are marching in straight lines; it's only when I use transform selection so as to position the rectangle over the graphic that they begin to emulate the edges of the graphic.

Maybe I misunderstand but when you transform the rectangular Selection what do you expect but having a transformed Selection as a result?

And Selections being pixel-based anti-aliasing on originally »binary« edges should not be unexpected (in accordance with the Interpolation settings).

Might you not be better served using Paths and Vector Masks?

Is the canvas rotated slightly? To check, press R  and check the angle in the options bar

Dave