Don't understand this logic, but you do what's right for you. I'm sure if we had real numbers to work with (balances, time horizons, etc.) we could put this to rest from a numbers standpoint.
Well, that's not what I did, but I'm just saying I can see the logic in it. I got into a financial bind back in the 90's, going through a bad divorce that left me with about $28,000 in credit card debt. I got help from Consumer Credit Counseling Service (CCCS) who negotiated with all my creditors, and put me on a 5 year plan to get it paid off in full.
Now, I might have had one or two small balances that I knocked off right away, regardless of the interest rate, but for the most part, I tackled the cards that had the highest rate first.
I was focusing on the big picture...getting that $28K paid down as fast as possible. And I did it in about 2 1/2 years. However, most people aren't like me...or most of the people on this board! Most people just look short-term, as in what the monthly payment is, without regard for the long term. And those people might be more focused on getting the monthly payment down. Or getting the number of creditors knocked down. I know when I was paying off that debt, I really felt good every time a creditor got knocked off the list, although I still concentrated on the big picture...the overall balance and how long it would take to get it paid off.
I've read that most people who go through those counseling plans end up failing anyway, so I don't always expect people to do the best thing financially. But I'd rather see them do the second best thing financially, if that's something their thought process can comprehend, than do nothing at all and fail.