Well, technically speaking the microwave frequency range is actually from 300MHz (or 0.3GHz) to 300GHz, so considering the examples provided and the frequencies in question I'm going to assume a Heating/Drying Industry context; because in reality, higher frequencies are used in other industries like space or communications. (source 1, source 2)
That being said, when you consider the heating of a microwave there are many factors to take into consideration, one of them is called the "Penetration Depth" which is defined as the depth below the surface of the material where the power density of a plane electromagnetic wave decays by 1/e (37%) from the original value at the surface. It's a technical definition that also involves a mathematical expression, but to keep things simple, the math implies an inverse relationship between the Penetration Depth and the frequency, i.e., the lower the frequency the higher the Penetration Depth and vice versa. (source 3)
Notice that it means they could actually go with a lower frequency, but maybe that implies design restrains and also even though it is stated in your sources as a broad generalization, that frequency isn't allowed worldwide. (source 4)
So considering this, it makes sense that they use a low frequency and also that make said claim.
PS: I'm a mathematical engineer who likes cooking, and wasn't expecting this kind of question here.