First, I am so sorry for your experience with your neighbors lil' Pug!
After reading your OP...I got to thinking about the mention that rigor mortis had already set in. From what I could find on this...rigor mortis normally begins to occurr about an hour after death, based on a 15 lb dog. In other words the smaller the dog the sooner the process begins.
It is very unlikely to occur 15-20 minutes later unless an animal was left in cold temperatures such as outside in a cold environment. Or, the owner discovered the deceased animal much later "after" death had already occurred.
As for your neighbors...sounds like they were not prepared for pet ownership especially with a dog who had special needs such as asthma...a true shame for this innocent Pug.
My heart just breaks for the life he surely deserved and did not receive.
Hugs,
Jo Ann