Those instructions are inaccurate. The temperature at bottling
may be the warmest the beer has gotten to but it may not be, particularly if you crash cool as the OP seems to have done (albeit only to 40F).
Bottling 101.
In every situaton one should use the warmest temp the beer got to after completion of fermentation and production of CO2 in the beer has stopped.
Once that has happened the amount of CO2 in the beer is governed solely by the maximal temperature reached. Know that temperature and you know how much CO2 remains and how much needs to be added.
Henry's Law is the basic physical law governing this not some instructions in a piece of software.
Since the OP is talking bottling, we can all skip the kegging comments to address his concerns directly.
Henry's Law: At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.
Even if the wort had completed fermenting at a higher temperature, when chilled and held at a lower temperature, the CO2 dissolved in the wort will come into equilibrium with the partial pressure of the atmosphere above it (nearly 100% CO2 for all practical purposes) since the head space in the carboy has been filled with the CO2 from fermentation pushing most of the rest of the gases out. [given that any starting O2 has most likely been used by the yeast and N2 is not soluble in wort]
If the amount of a gas dissolved in a fluid, such as wort, were dictated by the amount contained at the highest temperature it reached after fermentation ceased, then we could all breathe a sigh of relief, since the prospect of oxidation would now cease to become a concern.