In the weight training community, yoga is seen as problematic because it involves a lot of spinal flexion (ie bending the spine forward). This is seen as a general no-no (which is why sit-ups are generally viewed as bad as well today).
Stuart McGill is often quoted in these matters, as he has done extensive studies on the mechanics of the spine.
I'm not an expert on Yoga by any means, but in all the classes I've taken (and with the exception of the "relaxation" poses), the instructors have emphasized maintaining a straight back. Spinal flexion hasn't been explicitly encouraged, unless (perhaps) it was in the context of a forward fold, where the goal is to relax the muscles of the back after some other strenuous exercise.
Also, reading through your links, the McGill fellow seems to have a fairly nuanced position on core strength. It's not as simple as "don't bend the spine forward".
Those poses show spinal extension, not flexion. It may be the GP was using the wrong word here. I've never seen a yoga class that focused on spinal flexion, but there are a lot of poses that extend the spine, and if done wrong they can cause injury. Most yoga teachers know this, though, and encourage students not to over-extend, either by keeping abdominals active as you describe, or by focusing the extension on the mid- and upper-back rather than the lumbar.
On an only slightly related note, why doesn't gecko spell checker recognize flexion?
I'm also not an expert, but in the classes I've taken (gentle yoga and basic yoga), the instructors almost always guide us in poses that involve "spinal rotation."
Exactly. People don't understand that many of the yoga stretches are actually making them more flexible in a way that can lead to injury. A person should want their lower back to be strong and rigid (see planks and dead lifts as an exercises) and their upper back to be flexible. Every time I see someone doing yoga and really bending their lower back it makes me cringe.
Someone who knows more about anatomy than anyone I've ever met once said to me: "Half of all yoga poses are great if done correctly, and half of them should never be done by anyone." He mentioned the pigeon pose as a particular instance of a pose that may feel like it's "opening you up" but which, if you're doing it perfectly, is stretching something (hip ligaments) that don't need to - and shouldn't - be stretched.
EDIT: Downvoter, if you know otherwise, please educate me!
Why is there an appendix? Obviously the back is flexible to allow freedom of movement, but that doesn't mean a person should pick things up by rounding their lower back or make it more flexible. Another point is that nature did not make humans in order to have them sit in desks all day. In particular read the t-nation links in the OP.
I spend 15 mins or more of each workout combating the detrimental effects (incorrect pelvic tilt, shoulder impingement and rotation, etc...) of sitting at a desk most of the day.
To be honest, I have a friend who trains athletes (some pros like NFL, NBA) and he helped me out. You can look up many of the exercises using Google, but I would suggest finding a good trainer in your area and spending a couple hours with him/her. A couple hours working out with my friend help me understand what each movement should feel like, which was a big difference between doing it correctly and incorrectly. After that it's pretty easy to do by yourself, and most of the exercises only need a floor you can lay on, a wall you can stand against, and maybe some bands.
Stuart McGill is often quoted in these matters, as he has done extensive studies on the mechanics of the spine.
http://www.dailymail.co.uk/health/article-440309/Is-Pilates-...
http://www.amazon.com/Back-Disorders-Second-Stuart-McGill/dp...
http://www.t-nation.com/free_online_article/sports_body_trai...
http://www.t-nation.com/free_online_article/sports_body_trai...