The difference in reflectivity from either side of the foil is insignificant. Although it may be measurable.
Using a bare bulb thermocouple to measure oven temperature add a problem in itself. The infrared heat from both the elements acts directly on the low mass thermocouple and it skews the measurement causing it to read high and exhibit excessive variation. The only way I have seen reasonable measurements in my oven if to place the thermocouple inside a radiation shielding sleeve, otherwise the measurement trend shows wild variations. Somewhere I have graphs of with and without the sleeve. I saw differences of over 15 degrees with my thermocouple.
The mass of the thermostat sensor in the oven is much higher so as to normalize the effects of radiation so the air temp set point really shouldn't change. Imagine the difference in reflectivity just by adding the foil over the oven bottom, that could be significant. The dull vs shiny side surely isn't.
Of course the manufacturer will add wording in their documentation to not use the foil. This is all typical cover their ass boiler plate to limit liability. People do all kinda of foolish stuff and legal departments exist to protect the company. As long as the foil doesn't short the element or cover vents, physics is on the side of it causing no problem.
Damage to the inside of the oven or bonding to the porcelain? I could only see that if someone ran it through the self clean cycle of if the oven had concealed elements perhaps. Damage to the calrod bake element from radiation? I just don't see that, the thermal difference to the element could be no more then a few degrees, a small percentage of 1000 Deg F. [this post was last edited: 12/12/2015-11:10]