http://franklinmethod.com/latest-news/why-you-shouldnt-grip-your-core-part-2

Explains why pulling your navel towards your back and/or raising your pelvic floor while inhaling makes moving more difficult. Actually, the pelvic floor should increase tone while lengthening during inhalation (this is an eccentric contraction).

For what it's worth, I felt better following the instructions, and I suspect that gripping one's core muscles may be a result of emotional habits as well as a result of following bad advice.