Copied straight from the handbook:
REG108. GENETIC TESTING
REG108.1 If there is justifiable cause to question parentage of a foal, the Executive Committee may require the foal, sire and dam to be genetically tested, the expenses of which shall be allocated as the Executive Committee determines. The results of this test, together with other available information, may be taken into consideration by the Executive Committee in its determination of the foal’s parentage as recognized by AQHA. Such genetic testing shall be done by an organization approved by AQHA.
REG108.2 The owner or lessee of a stallion exposed to one or more mares, shall, at his own expense, file with AQHA a written report of the stallion’s genetic type, obtained from a laboratory approved by AQHA, and in accordance with procedures adopted by AQHA. Once such type is filed with AQHA, it is not necessary to repeat such filing annually, except as requested by AQHA. This type must be on file with AQHA prior to the registration of any foal sired by such stallion from mares covered in REG108.3 below.
REG108.3 A genetic type must be on file with AQHA for any mare foaled on or after January 1, 1989, prior to the registration of any foal produced by them.
REG108.4 All stallions having 25 or more mares on their 2014 breeding report are required to have a genetic disease panel test on file with AQHA prior to the registration of their foals resulting from breeding’s occuring after January 1, 2014.
REG108.5 All stallions are required to have a genetic disease panel test on file with AQHA prior to the registration of their foals resulting from breeding’s occuring after January 1, 2015.
And here's a link to the online version: AQHA Handbook
That way you can look at it yourself and see if you can find it anywhere. Note that in 108.1 & 108.2, it says an approved lab. It does not specify that in 108.4 or 108.5. It just says the tests must be on file, not that the lab must be approved nor does it specify UC Davis.