It most certainly is true and it's quite simply how any and every transformer works. A transformer has a ratio, and converts not only AC voltage but also impedance. The calculation is the impedance A reflected on the primary winding of a transformer is the impedance B divided by C squared, where C is the turns ratio of the transformer and B is the impedance loaded on the secondary winding.

This is the key factor with moving coil step-up transformers and although it's straightforward, it seemingly often gets ignored or not worked out correctly. For example, a normal MM phono stage has an input impedance of 47K ohms. If you use a 1:20 step-up, then the impedance on the primary winding (so what the cartridge 'sees') is 47000 divided by 20 x 20, therefore 117.5 ohms. With a 1:10 step-up the cartridge sees 470 ohms, and although 1:10 may appear more suitable in terms of gain, if the cartridge works ideally with around 100 ohms loading, 1:20 will be better. Every system has a volume control, so a source that is quite high output isn't a major issue.

It's only more complicated with a TVC because for every volume setting, the ratio will be different. However, as Geoff points out, the ratio is 1:1 at maximum volume, so effectively the output imedance of the TVC is the same as the output impedance of the source. At any lower voume setting, the output impedance will be lower than that of the source, which will never be a problem.

The 'golden rule' is 1:10, in terms of source output impedance and power amp input impedance. I've seen some people suggest that the higher the ratio the better, but there is no actual point. In fact, you can probably get away with as low as 1:5 before there is any audible effect in most setups, but 1:10 is sensible and avoids any potential issues with frequency extremes or attenuation.

With an active preamp, the output impedance of the preamp needs to be taken into account. With a TVC, the output impedance of the source needs to be taken into account.