Here is a second topic that I am researching. If anyone has any opinions and/or research they think could be beneficial to me in answering this research question, please do add it in an answer.
I haven't seen much on Kinesio tape and injury. Here is one that may help. From the performance and balance studies I've seen kinesio tape hasn't shown statistically significant benefits over traditional ankle taping.
Adam Skinner
Article Peroneus longus activity in different types of taping: Athle...
I came from more than 20 years of sports rehab and functional evaluation. After a basketball (or other sports) ankle injury the most important thing is to do a good rehabilitation path, focused in particular on dynamic and static proprioceptive training (possibly with biofeedback for the patient), followed by an objective assessement of the functional recovery (you can use different kind of technologies). Every kind of tape are useful only in the first phase of sports comeback to support the athlete. Our goal is to recover a complete functionality of the injured part (this is a general issue) without external support. A good rehabilitation must produce a complete recovery of strength, proprioception and ROM (Range Of Motion)
In my experience, KT is very valuable throughout the recovery process for stability, pain control, and proprioceptive feedback. While I haven't used KT on any basketball players for ankle sprains, I have used it on discuss throwers and hockey players. Unlike the traditional "athletic tape" used to stabilize an injury (which looses ~50% of his support after a 30 min warm-up), the benefit from KT is a prolonged proprioceptive cue. It doesn't really limit the mobility of the joint, but does provide a tactile cue and supports the injured musculature. The compression helps for pain control and sense of increased stability. As Fulvio Stradijot mentioned earlier, the most important part of ankle injury rehab is static and dynamic proprioceptive stability as well as return to functional use. Where I've seen the benefit of KT over traditional taping is in the facilitation of full return to sport without structural support (restricted ROM) providing for improved functional/dynamic challenge of the injured appendage.