I would perhaps be concerned about attending a Yin Yoga class too, if the teacher was directing everyone to just flop into a pose. I suspect that whoever wrote the article was being sarcastic, if he did indeed use the term flop.
There are many styles of yoga that are not alignment based but are still very valid forms of practice. (Bikrams, Ashtanga and Kundalini, just to name a few.) The alignment based teachers generally come out of the Iyengar tradition and can be very demanding about their belief that alignment is super important and the only way. Personally, I believe that their intolerance towards other styles is not healthy nor helpful: Mr Iyengar himself is very open to experimentation and doing whatever is necessary to help the individual student, but many of his students (perhaps because they don't have his vast experience and talent) copy his instructions without understanding why he has given these instructions. Without this understanding, how can they find out what is actually best for the student in front of them right now?
Every body is different: you cited an article earlier by Paul Grilley. Paul has done a lot work trying to dispel the myth of alignment based instruction that assumes there is only one way to do a pose, that there is a best way to do yoga. See his Anatomy DVD or check out his web site for pictures of bones of different people: there is no way that everyone can do every pose and what is good alignment for one student is really bad alignment for another student. To give just one illustration: most alignment based teachers insist that the front foot in poses like Warrior or both feet in Mountain pose should always be pointing straight ahead and that the knee also must be aligned pointing straight ahead. These are good general directions but they are not universal directions. Some students have a
torsion (a twist) in their tibia that cause their feet to point outwards. Trying to force these students to turn their feet parallel and pointing forwards means that these poor students have to twist their knees inward considerably, which is not only uncomfortable, but also dangerous to the knee ligaments over time.
Alignment is a good idea, but there is no universal direction for aligning a body that works for every body. Always is always wrong and never is never right. In my Yin Yoga classes I am concerned about alignment, but only with each individuals own particular alignment. I don't ask students to "flop" into any old pose but give directions how they might enter each pose. Then I check the whole class to see who may be struggling or confused: I then ask that particular, unique individual what she is feeling. Only she can tell me what is the right alignment or position for her. Aesthetics has nothing to do what is right: aesthetics just looks good, but it could be harmful. What are you feeling? That is the only way you can know whether what you are doing with and to your body is helpful or harmful.
It keeps coming back to your intention and paying attention. If your intention is to look good, then you won't care whether what you are doing is healthy for you. However, in your case your concern is for your health, so forget how you look in a pose and check out whether this pose feels right for you. Is there pain? Do you intuitively and instinctively feel this pose is just not right? If so, change it! Ask you teacher for some options. There are always options: that is why we have so many different poses - if one doesn't work, we can find one that does.
In your situation, I would talk to the teacher before class and explain your concerns and your challenges, then while you take the class, be your own teacher and doctor: continually ask yourself if this feels right or not. If it doesn't feel right, wave the teacher over. Of course, in Yin Yoga, you will be challenged - don't bail on the pose just because it is juicy, but if you really know that this isn't right, then act.
Hope this helps
Bernie