Stretching does not reduce soreness, it increses it. Soreness is due to microtears in the muscle fibers caused by exercise. Stretching can also cause microtears.

The only way avoid getting sore is to increase your load progressively, or stay at a load you're accustomed to.

Being flexible might help with soreness in a sense that the soreness is less noticable: for example if you have very tight hamstrings, and they are sore, any movement is likely to make that soreness noticable. If, however, you are quite flexibly you might have to stretch your hamstrings, by bending at the waist, before you actually notice that you are indeed a bit sore after yesterday's workout.

The title of the article is too generic - he is talking of static stretching before a workout which is largely useless for weight lifting or power lifting styled workouts. In those regards the author makes a fair point. Static stretching before lifting weights affects stability. Plus it does nothing to warm up the major muscles that are used when lifting the weight.