Depends on what he means by "loses money."

If they weren't making enough money to cover costs, it seems to me that they'd either raise the price of media mail or do away with it to make people use first class.

I guess they "lose money" in the sense that they would be making more off the packages if people were paying the first class rate, instead of the media mail rate, but I can't imagine that they'd still offer the service if it was costing THEM to keep it going.

Anybody else ever heard this?

Dont they "lose" money every year? On everything?

Yes, it is said that the rate for MM is less than it costs them to deliver the package. I don't think they take into account that MM goes only when there is room so that space would be travelling empty and they'd be paying the clerks and the sorters to be there whether they have MM or higher rated mail going by them. To me it is additional revenue without significant increase in costs.

its because some people use media mail  for items that should not go media mail. 

For example on Ebay right now there is someone saying they are shipping scrapbook page protectors media mail.

It is being abused.

Or it could be due to the route taken.  Here's an actual book, mileage by MapQuest:

If I were driving:  Brazil, Indiana to Avon, Ohio - 370 miles

The USPS route:

Brazil to Hazelwood, MO - 195 (oops, wrong way)

Hazelwood, MO to Warrendale, PA - 620 (was that Ohio back there??)

Warrendale, PA to Avon, Ohio 135 (success!!)

Total USPS miles - 950

Gosh! Sharon! No wonder the USPS is losing money with mileage like that! I wonder what "brain" thinks up these routes. It would be interesting to know the whys of such routes. Does anyone know?

A lot of the "excess" mileage is caused by packages having to go through specific local and regional sorting and collection centers.  No package or letter ever goes direct from one PO to another because that would be incredibly inefficient.  Instead, mail gets collected and sorted then bundled together with other mail going to the same area.