Sure, why not? People play with bone contusions, stress reactions, stress fractures, non displaced fractures, etc. all the time. They are all along a spectrum of the same thing. Small microscopic fractures of the bone trabeculae (contusion/reaction), it gets a little more serious and you may see a fracture line macroscopically on X-ray or MRI (stress fracture), and then the displaced fractures that often eventually you can't play with and need surgery. The distinctions are very blurred until the end stage when the fracture is obvious.
Athletes play with pain all the time, often quite well. Of course there is a point at which eventually they can't continue, but it wouldn't surprise me at all if Kyrie already had a stress reaction/stress fracture of his inferior patella that was diagnosed as "proximal patellar tendinitis with some abnormal bone marrow edema at the inferior patella" (essentially "jumpers knee"), and eventually that inflamed piece of bone completely broke loose in overtime of Game 1.
Painful, sure. But not unstable or painful enough to prevent him from potentially playing well until now.
As far as what the team docs told the team and what they told Kyrie. who knows. Not always the same thing. Professional sports medicine is high stakes, and there are often conflicts of interest. Players' long term best interest is not always top priority unfortunately (they should probably get second opinions more than they do).