You don't give a part number for the NAND gate, so we don't know if it has hysteretic inputs. And, usually there is a resistor in the feedback path for more control and stability of the oscillating frequency.
Beyond all of that, the oscillator probably is producing a symmetrical output, which looks the same on a scope inverted or not because of how a scope trigger works. The extra inverters are merely a delay line, giving a time-shifted (not inverted) image.
What is the purpose of R1?
ak