Short answer: there is no best long-term sitting posture. If there is any, take care of posture (I'd risk to say upright is best), and move every certain amount of time in the chair and/or around.
I'm for positive responses so let me elaborate a bit more. All cautious considerations, as kenorb
properly states, are ok. However, even if some of those considerations attend to the actual question, which was what should I DO when sitting? (notice the question was not pointed so much as to what NOT doing). What follows is an intent to give further argumentation in how to achieve the goal of sitting in a way that can take care of good posture in general, how and mostly why.
Rather move around once in a while, and shift between different subtle positions. When you are sitting for long, you don't want to atrofiate your muscles, nor your posture. Hence several considerations:
Check the post sitting is the new smoking, and the main answer: The solution is simple. Move.
Consider that what you need to take care of when sitting is your whole body/organism, and not just a part.
When sitting backwards you can alleviate your lower back for a while, but doing so as a norm can weaken that area as well.
Remember that the human posture, standing or sitting or moving, has a certain balance. We have anterior and posterior muscles surrounding our body to make this balance possible. This is why I would infer that if one has bad posture (not necesarily back problems) along the day...reclining can be more easy going. But in the same coin, in the long run this may not favor good posture and a distributed and balanced muscle development.
The study you mention says that the 135-degree posture, suggesting less strain is placed on the spinal disks. Of course this may be true, but to conclude from that that it'd be best to not sit at 90º is rather far fetched. I figure in some way that the article suggests that maximum relaxation can always be best. But in reality: (if we assume not to be jello floating in a liquid environment) we do need a certain amount of tension to function properly. Remember the fat moveless couch potatoes from the movie Wall-E that underdevelop muscles and even bone-structure.
Again, the reference you take mentions volunteers with healthy backs, this ussualy means that they'd have no problems in that area, but I'd argue that not many people reach a full healthy posture in a broader sense.
See what kind of chair you have available. Some may favor a certain way of sitting or several.
Also, Galen Cranz's been researching chairs: here interview and book reference.
Since many people don't only sit, but also are in front of a pc let me add:
If you can use a keyboard near your lap, this can be better than having it a higher level. I find the latter to thrust your elbows, shoulders, upper-back and neck upwards.
Consider, like apple co-creator Oz Wozniak did: Dvorak's effort and resulting keyboard configuration. The main aim there is not for speed but for comfort, and avoiding carpal tunnel syndrome.
Bashir w[Author] AND 2006[dp]
yields two studies, neither of which exactly match the BBC description. Jez, if you have a better idea, let me know. I don’t feel like I can answer without evaluating that study.