As a disclaimer: I was not there, I cannot make any clinical judgments, etc. This is all purely hypothetical.

Legally speaking, the owner should have pushed for an autopsy. While physical exams and clinical history allows us to make presumptive diagnoses, in the absence of something glaringly obvious (gunshot wound, known toxin exposure, previous diagnosis with something fatal, etc), we cannot be 100%. That being said, we can get close to 100% certainty. There are plenty of signs on physical exam that would make myself or a vet 90%+ certain that heat exhaustion/heat stroke occurred (fever, blood in colon, blood in urine, breed, mucous membrane colors, etc). Bulldogs, being the mess that they are, could pass away from respiratory distress or heat exhaustion, even on relatively mild days. It could have been something primarily cardiac (as in, heart disease leading to death instead of heat exhaustion leading to cardiac arrest), or it could have been something entirely different- someone telling you their dog is healthy is both relative (it's a bulldog, they start out diseased) and potentially misleading (he's never needed to go to a vet in his life!).

But otherwise, the kennel owner is SOL. No autopsy was performed, so there is nothing to confirm or contradict the presumed cause of death. Even if one was performed and showed some horrible, unpreventable, immediately fatal disease, you have word of mouth that would have affected the business regardless- people are much more swayed by emotions than they are cold hard facts (look up the whole Trifexis and Atlanta debacle that comes back up every year or so- autopsies and clinical experience essentially debunked that).

For your other question, essentially heat exhaustion is milder than heat stroke- if corrective actions (cooling off, taking inside, water, etc) aren't taken, then the internal temperature/organ temperature continues to rise, leading to heat stroke.