Honestly, my opinion is probably quite similar to the prolotherapy, with the only caveat that at least theoretically there is a bit more oomph behind this one than simply injecting hypertonic saline into a degenerated tendon.
The proposed mechanism here is that you take the body's platelets and inject them into the degenerated tendon, then use the healing properties of the proteins in the blood to spur healing.
There are no good randomized controlled trials, only small cohort studies of patients who self-select (meaning they'd already decided to have the therapy...which means they approach the treatment with a bias).
My personal thought, as both a biomechanist and a pain scientist (my post doctoral work has been in the neurophysiology of pain), is that it isn't going to pan out with further scrutiny...and neither will prolotherapy. My reasoning is that histologically we see the tendon actually becoming disorganized as it degrades: instead of nice, neat parallel fibers that should pull in relatively uniform ways, we have a disorganized glob of tangled collagen that cannot pull effectively, and without triggering an overwhelming pain response. Think of tarp lines and how awful of a pitch you'd get if your guy lines were all tangled up and you tried to pitch anyway.
Simply inducing an inflammatory response, or in the case of platelet- rich plasma therapy actually trying to induce a "healing" response directly, is not going to reorganize those collagen fibers. There is a well-known maxim called Wolff's Law that the body responds to stress by strengthening and reoranizing along the lines of stress. A medical intervention for a mechanical problem doesn't strike me as imminently successful. Surgically you can cut out the degenerated part; mechanically you can induce a noxious eccentric loading to force a reorganization of the collagen (actually rather successful for many people, good RCTs for the knee, Achilles, and lateral epicondylalgia); and from a neurophysiological perspective we are finding some amazing changes in the central nervous system that may affect muscle behavior...which might be why the tendinopathies are happening in the first place. But that's a whole different and way more complicated conversation. But one I love to talk about, by the way. I am a nerd in more ways than my gear closet!
My long, beleaguered point here is that tendinopathies are terribly complicated, we have no really reliable ways to treat it, don't ever allow a clinician to inject cortisone into any TENDON of your body (it can be injected elsewhere...at least for now), caveat emptor in medicine (oh how much ripping off goes on in the doctors - and PT - office!!!!), and there are tons of great research projects going on that will give us more tools in the near future.
I'm guessing several of you have some tendon issues...if you PM me I can send along some descriptions of the eccentric loading protocols for you to try (if you haven't already...) for your particular body part. I'm happy to help...and it costs you nothing but your continued advice on how to lighten my pack ;)