In the frequency sprectrum, when LPF corresponds HPF, it becomes 'crossover'. Therefore, the "LPF for LFE" IS part crossover, between the sub and rest of speakers, by its very definition.
Neither is right and neither is wrong and both are on the extremes for this setting.
(I am ignoring room interaction based serendipitous correction of the following discussion on inaccuracy of signal processing due to poor crossover settings.)
What is of critical importance is that between the HPF on speakers and LPF on sub, there should not be big enough separation that a FR dip is created. If the LPF is set at 40Hz and HPF at 120Hz, roll off slope aside, no speaker/sub will get signal at frequencies in the 40-120Hz band. This will most likely create a big dip in the FR plot. I encourage both to validate this is not happening in your respective setups. I hope not, but it never hurts to confirm.
The opposite case is worth mentioning too, LPF at 80Hz and HPF at 60Hz. This creates a situation where the both, speakers and sub, are getting signal at frequencies in the 60-80Hz band. This would most likely result in a peak around those frequencies.
The 'crossover' concept makes sure this does not happen because LPF freq = HPF freq. By rolling off the HPF and LPF at the appropriate rate, albeit, in opposite directions, the sum of sound from the speakers and sub is maintained at full signal level without creating a processing induced peak or dip.
More on crossovers.
