Your breakpoint locations should then be determined solely based on where your particular site design 'breaks', i.e where it needs a layout modification, in the continuum between your chosen min and max widths.
That would be correct. Every Design is different and you have different elements that need to be corrected at different screen widths. That is why you should not dwell on where to place a breakpoint. You place the breakpoint where the layout needs it to be, not where people normally put it.

Design outside the box.