Thanks to everyone who provided relevant answers. Full disclosure: I am an electrical engineer so I was able to sort through the answers where people made statements that were irrelevant, or just plain wrong, in their explanation and dismissed those outright. Among the remaining responses, I would summarize them as mostly gravitating towards the notion that running the engine while attached to shore power as not being an issue, and nobody shared a story of that ever causing a problem. However, one dissenting opinion seemed to come from a contributor who is very experienced, very prolific on this site, and viewed by some here as very knowledgeable.
This morning, I called the company who published the original article (a very well respected company in the RV industry, I might add) but after being bounced around to a couple people, I still wasn't able to find the person to take responsibility for writing the article or to provide reasoning or justification for what they wrote. The last person I spoke with took my information and said he would look into it and get back to me, but I'm not holding my breath.
So next, I decided to call my RV manufacturer (Thor) and see what their tech support people recommended. They said using shore power while the engine was running isn't a problem and that it could even help with jack operation. I'm not going to recommend this solution for every RV because it clearly depends on how systems are wired and what components are used.
"Never start your vehicle or run the generator while you are plugged into shore power."...fable, lore, or fact...I don't know. I'm going to continue my RV hookup and unhook process the way I always have. It never has caused me any problems, and fundamentally, the way I've been doing it seems intuitively sound to me.
