Yes that is true. But weed whackers (string/line trimmers) are not tools to get rid of weeds, only cut them back, no more than any lawnmower. Although you can get the roots fairly well if you dip the line into the soil but you'll damage any nearby plants that way.

If you want to get rid of weeds, you'll need to pull, dig, spray, etc. Trimmer are mostly meant to knock things down to make things look nice or clear paths.

As far as a weed whacker eliminating weeds, depending on the type of weeds, if the whacker is used before a weed went to seed, it might eliminate or at least not spread that type of weed seed.

However, if one has a tap rooted weed, whacking off the top will only strengthen the weed.

Gardenbud, Faye

Most rotary lawn mowers are not designed to cut tall grass, i.e. anything over 6". If a mower is used on a regular basis to cut tall grass, the bearings will get damaged.

String trimmers are a good tool to cut tall grass.

String trimmers don't cause weeds any more than chains saws cause tree seedlings.

You can use weedwhackers to trim large areas, either with line or blades. I don't see how they would encourage weed growth more than anything else, except perhaps because there is a tendency to cut too close to the ground when clearing with a whacker, leaving the grass cut back and getting sunlight down to the soil, creating conditions that certain weeds find preferable for vigorous growth.