DeLuca offered his own solution to the whole mess.

"If I were in charge of the government, I would index the minimum wage to inflation so that way everybody knows what they can count on. The employees know they're going to get increases on a regular basis. The management knows that they're going to have to pay a little bit more with inflation. It just seems much more sensible and fair to me. I don't know why it hasn't been done like that. I would do it that way because in the long, long run it's going to approximate the change in inflation."

DeLuca and Little were engaging in a somewhat serious discussion about the recent battle around minimum wage hikes. That's what led up to the minimum wage suggestion. DeLuca's view was that minimum wage increases happen — they've been happening throughout the four decades he's been in charge at Subway, and it's just part of the fast-food experience, he said.

"When I started in the business, the minimum wage was $1.25. I've seen an enormous number of wage increases. Basically it applies evenly to everyone in the business. This increase would impact Subway plus every other competitor so it would not put any brand at a particular disadvantage. It might have a slight impact on consumers because what's going to happen is a wage increase will happen and all the restaurant owners will have to recoup that somehow, usually through a price increase. It might make eating out at restaurants have a little bit less competitive advantage compared to supermarkets."

Then Little guided DeLuca into a bit more controversial waters. She noted that CNN had reported that Subway racked up more wage and hour division violations that any other fast-food chain, and she wondered how DeLuca felt about that.

CNN, relying on Wage and Hour Division records from 2000 to 2013, said it found about 17,000 Fair Labor Standards Act violations that resulted in franchisees having to reimburse Subway workers more than $3.8 million over the years. McDonalds and Dunkin Donuts were Nos. 2 and 3 on the list.

But, as with the minimum wage increase, the wage and hour violations didn't seem to lead to acid reflux during DeLuca's response.

"I saw that, and I think that the headline is not quite accurate," he said of CNN's story.

"When I read it," he told Little, "I said 'Oh, it looks like they're writing that our wages are lower than the wages of other places.' When I read through it, I saw they were talking about wage violations at the store level.

"So a couple of thoughts: First of all, the fact that we have so many stores has an impact on how many violations there are. If we had 5,000 stores, there would be a smaller number than if we had 25,000. … The vast majority of our owners are doing the right thing but some are not. I would say this. We, as a company, realize that some of our owners have not done the right thing. I can't tell you exactly why, but I think we have a lot of first-time business people that enter into business in Subway, and they might not be as sophisticated in what to do.

"So a couple years ago, maybe three or four years ago, we started working closely with the Department of Labor to partner with them to help educate our owners on the right thing to do. The people who come to work deserve to be paid properly and there's no excuse. I could understand someone making a small error but sometimes people make systematic errors and that's not right."

Also read:

GOP blocks minimum wage plan
California unions target $13 minimum wage
Obama invokes Henry Ford to urge minimum wage boost