Nonoise is correct, and certainly no artist, whether musician (singer) or actor, would disagree. In fact, they wouldn't even consider this hairsplitting. Thiel, teel, and teal are indeed pronounced slightly differently. Perhaps inflected might be a better term?
I also wonder that if someone does not agree that there is a difference, and an important one, between the sounds of these three pronunciations, then should that person be trusted on their opinions about audio reproduction system subtleties, which are quite a bit harder to hear in many cases? This is reminding me a little of a guy who thought he could hear very subtle differences between two different tone arms used with the same exact equipment, yet could not distinguish the difference between a violin and a viola, or a French horn and a trombone.