I would not regard that author as focusing on strength. Instead, her experience speaks to "weight loss and wellness" camps, where the need for a rigid trunk during maximal and near maximal exertion is not necessary.
What probably is worth highlighting in a weight loss camp however is proper breathing, since it's primarily an aerobic (with oxygen) affair.
To be fair, the debate is still on with the Valsalva Maneuver. A 2006 study studied it a bit and summarized:
Although breath control was shown to influence intra-abdominal
pressure, it does not appear to influence isometric trunk extension
force in a knees bent position. Further, the intra-abdominal pressure
produced in such efforts appears to be unrelated to the amount of
What I would add to that though is that the reasoning espoused by most lifters (and most vocally Mark Rippetoe) isn't necessarily about force production but rather spinal protection. Here's a decent video from Ripppetoe explaining his views on it.
Basically, by filling the lungs and tightening the diapgram and abdominal muscles, you're bracing the lumbar and thoracic spine, providing less opportunity for it to shift and get damaged.
This is not a concern for the strength loads involved in a "weight loss and wellness" camp, but it certainly is for strength athletes.