Once it flowers it makes no difference if you weed whack or not. It will spread seeds around either way. The advice you should have heard was to ensure you chop it down before it flowers, which is not the same as saying don't chop it after it flowers.

Even if Garlic Mustard, or any other plant, flowers but has not yet been visited by pollinators or the plant has not yet developed viable seeds you can cut them down. Cutting any flowering plant once it has developed viable sees can spread them around to produce more plants in the future. The advice given is assuming people are not smart enough to tell when a plant has developed seeds.

kimmq is kimmsr