Edible perks such as donuts and pizza often accompany administrator visits in some districts, says the report, quoting Keith Reed, a fifth-grade teacher in Joshua Tree, California, who says of administrator representatives, "They always bring food. It makes you feel as if you are in a relaxed atmosphere and that they are looking out for you."

But the truth, he has concluded, is different. After a workshop run by the California Teachers' Association union in 2013, he says he was shocked at the level of fees charged by his plan and switched investments that came with a 2 percent fee to some that cost 1/10 as much. In the report, he adds, "The adviser in the lunchroom is there to make a buck."

Not only did many of the investments come at a considerably higher cost than others, Reed said in the report, but investment advisors would often defray administrative fees in exchange for opportunities to pitch investments to the teachers.

It might be surprising, particularly after the huge (and still ongoing) debate over the fiduciary standard, to learn that teachers—served by 403(b) plans, not 401(k)s, and often populated by annuities as investments—don't get the benefit of an obligation on the part of plan administrators to put them first.

And assuming that their school districts do so is making a mistake. And as a result, investments in 403(b) plans come with considerably higher costs than those in 401(k)s—and therefore reduce investment gains for account holders.

Says the report, "Annuity buyers can pay as much as 3 percent of invested assets in fees each year. In contrast, fees on 401(k) accounts average less than 1 percent annually, according to BrightScope Inc., a firm that tracks retirement-plan data. For $100,000 invested for 25 years at 6 percent, an extra 2 percentage points in fees would cut 38 percent from the final account value."

So how widespread is the problem? Third-party administrators being paid by investment providers are common enough in the teaching community that in California alone, more than 200 school districts have the same third-party administrator—which does not charge the districts for its work but, says the report, "is paid by the companies approved by school districts to provide investments to workers."