George you are right and wrong. True that "accredited" may not be the correct term to use. To be accredited in the state of Missouri we would have to offer degree program that included mathematics, humanities, etc. All of the things that a four year University offers. "Certified" is more appropriate to taxidermy schools.
That is not to say that we can just pay and be on someones list. I can not speak for other schools in other states. But here in Missouri, we are required to undergo very strict, lengthy, annual recertification process. Our facilities, curriculum, and staff qualifications must be updated, submitted, and approved by the Missouri Department of Elementary and Secondary Education, each year. We do not advertise as being "accredited". We are a "propriertory" (trade) school recognized and "certified to operate by the Missouri Department of Higher Education".
We also undergo invasive on-site inspections. A team of education officials travel from the capital, and spend two days going through every aspect of our school. From interviewing present and former students, and staff, to checking records and curriculum, to making sure that we have enough antlers, fleshers, cordless drills, blowdryers, fire exinguishers, etc. We have a very high level of standards that we are required to meet.
Chip Stamper
Missouri Taxidermy Institute
www.taxidermy-schools.com 
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