That explanation is on the right lines, but a bit confused.
Every radio since the 1930s - and by every, I mean most - is a superhet. It works by converting the range of frequencies on the dial to a single frequency before amplifying, filtering and turning it into audio. (The invention of this idea was like the invention of standard containers in shipping - suddenly, all the hard work could be got right just once, no matter what was being shipped.)
It's very easy to convert a range of frequencies to a single frequency. You just arrange to generate your own very weak radio signal at a fixed offset from the one you want to receive, and then mix your signal and the received signal together. At that point, you get a lot of different stuff out - but mostly, you get a signal at the difference between the two frequencies.
Change your local frequency, which is easy to do, and you change the frequency you're picking up. The difference between the two is what you then amplify, filter and turn into audio - which is quite hard work, electronically, but made much easier if you just have to do it for the one frequency.
So, if you want to pick up signals between 88 and 108 MHz, which you do for normal FM, you create a signal inside your radio between 98.7 and 109.5 - always 10.7 MHz above your wanted signal. IThen, you do all the hard work on the fixed frequency of 10.7 MHz.
Tune into 97.4 on the dial, you're tuning your local radio signal to 108.1. The difference is 10.7. But there's also a difference of 10.7 between 108.1 and 118.8 - which is a standard aeronautical voice frequency (used by Glasgow Tower, I believe). If the radio isn't good at rejecting frequencies above 108 MHz (and cheap ones aren't), then you'll get both your wanted FM radio station and any aircraft on 21.4 MHz above that station, at the same time.
It gets worse. Broadcast FM signals are quite wide and it's not uncommon for FM radios to receive 200 kHz (0.2 MHz) or more either side of the central frequency at once. So when you're listening to 97.4 you can pick up everything from 118.7 to 118.9 MHz. Manchester Tower is on 118.625, which is a bit outside that range - but certainly not outside the bounds of probability that a cheap FM radio will pick up a nearby aircraft transmitting on that frequency.
(Incidentally, that's a major reason why you're not allowed to use radio receivers in the cabin on flights - FM radios generate signals that fall within the VOR band, and that could be bad....)