This depends greatly on the method of heat transfer. Your
explanation due to the colour applies only if radiation is the
dominant path for heat transfer.
In the case of the saucepan over the fire, we can expect the
following:
1) Conduction
Not very great because of the layer of air between the flame and
the saucepan.
Air is a bad medium for heat transfer by conduction.
2) Convection
Some convection exists, but not a lot as compared to radiation.
This is because the distance between the flame and the saucepan is
too short.
Radiation is a much more effective method of heat transfer.
3) Radiation
As mentioned in (2), radiation should be the dominant pathway for
heat transfer in this case.
Thus, we will expect a dull black surface on the outside of the
saucepan to boil water faster than that of a polish chrome.
Anyway.... Saucepans are usually black in colour, I believe. It is
pots that have more silver colours... mainly because they are used
to maintain the heat of things like soups within them...
Regards,
Eagle
Owner of Strategic Tuition