The local oscillator frequency can be above or below the signal frequency.
The IF frequency can be above or below the oscillator frequency.
Now consider a simple AM broadcast receiver, this probably has an IF of 470khz and receives signals in the ranges 150 to 285 khz (the long wave band) and 530 to 1600khz (the medium wave band).
In the long wave case the local oscillator could tune from 320 (470-150) to 185 (470-285)khz. If you calculate this out throughout the range of frequencies, you will see that when trying to recieve 235 khz, the local oscillator is on 235 khz.
Not a good situation for a receiving an intelligible signal, the local oscillator will be much stronger than the received signal and prevent it from being heard.
Now, if the local oscillator is set to be above the signal frequency, it will run from 620 (150+470) to 755 (285+470)khz, and at no point will the local oscillator be on the same frequency as the required signal.
The same applies to the medium wave frequencies, try calculating it out.
However, if we have a fixed frequency VHF receiver tuned to 156Mhz, with an IF of 10.7Mhz, the local oscillator can be on 166.7Mhz (156+10.7) or 145.3Mhz (156-10.7).
Either frequency will work no problem.
JimB