1) There are live adenovirus vaccines currently in use (e.g., https://linkinghub.elsevier.com/retrieve/pii/S0264410X163061...).
2) People report being sick from inactivated vaccines so those carcasses you mention evidently still trigger symptoms, and according to Wikipedia "most" viral vectors are designed to be incapable of replication so presumably some could transmit. Additionally, at least with Sputnik botched inactivation had been reported (by Brazil, https://www.dw.com/en/brazil-was-there-sloppiness-with-the-s...). Frankly if I get symptoms and am contagious then I will consider myself infected for all intents and purposes.
In the end, though, we can engineer non-transmittable viruses if warranted, and with proper care we successfully do so. I don't know the approach taken with the cancer-fighting virus in question but I bet proper care had been taken.
Technically you aren't incorrect but presenting the information like that is disingenuous.
It's been a while since I read the book, but it makes sense to me people failed to identify with the doctor as the bad guy at the end of the movie.
In the book, we're shown what amounts to a small love story between him and a vampire, and the living-vampires brutalizing the dead-vampires, and finally the doctor.
There's a ton of build up to the reversal that the alt ending does not seem to have.