Determining equivalent resistance to find the cutoff frequency
Am I correct in thinking that the equivalent resistance for the LPF is
  ~0.01Ohm, due to the output impedance of the MAX6250 at low
  frequencies?


Nearly correct because, the output impedance will rise with frequency increases (see page 7 of the data sheet): -



So, if you had a noise problem at around 100 kHz the output impedance is 10 ohms rather than 0.02 ohms (10 Hz to 100 Hz). This might make you rethink the value of the capacitor and you might indeed pick a lower value AND that capacitor may perform better because, being lower in value, it will likely have a higher self-resonant frequency.