Yesterday, I was running my dishwasher while I filled up the sink with water to do some cleaning in the kitchen. I finished up and pulled the plug in the drain, and when that water started to drain (about half of my double sided stainless steel sink) the drain in the basement started to back up. The overflow was the contents of the sink. This has happened twice in the last month.

I called a plumber to come and look. He brought an auger in and before he even had the main cap off he was telling me "This is the most powerful cutter out there so if it stops up you don't have a clogged drain, you have a busted pipe". And Lo and Behold - he said the auger was stopping up. I'm not sure what was going on under the ground, it sounded like metal grinding against metal. But when he pulled the auger out, there was no mud, no nothing gunked up around the end of it.

The next thing I know he's upstairs with me, talking ahundred miles an hour about calling my insurance company and this is what you tell them, blah blah blah. I just felt a totally wrong vibe coming from this guy. There was no discussion of scoping to see the extent of the breakage - I mean - aren't there some kind of injectable things they can do? I feel like this guy was just a fast talking weirdo out to do the most expensive type of work.
So my question is, what are the possible causes of this backup. If it is a broken pipe, would an aguer get completely STOPPED because the belly of the pipe was disintegrated? If it is a broken pipe, and it was stuck in the "disintegration", shouldn't there have been some clay or mud or something on the aguer? Even if the belly of the pipe was broken, isn't there other options besides tearing up my basement that could be explored? Or at least discussed? Please Help!

Before you do anything get a Sewer Cam ran through there to see exactly what you have, As a rule, but not always, you'll see some dirt on the auger if you have a broken line but there isn't a plumber going that can tell you for sure what's going on under ground. Run a camera through there and make your decision then. Don't let any body fast talk you into a hasty decision.
Good luck, Tom

Yes, a professional will run a cam though before they start calling it a broken line.

I had a similar thing from one of the national companies, turned out just some serious root issues. We still dug it up, put in a additional clean out and dealt with root issues but I refused to pay the first guy because of the scam he was running.

I'm inclined to agree with you. Call another plumber.