Your reasoning is correct. It is very unlikely that your stallion could be carrying the red gene and has not yet transmitted it. The matings you describe are an example of a highly informative cross that geneticists call a test cross. If your stallion had been bred to 10 bay mares and not had a chestnut foal, you might want to use the DNA red factor test because the data set is not as statistically compelling in such a situation. The direct gene test provides answers more quickly than breeding tests, in weeks rather than years, and can be applied to young horses without a breeding record.
Black horses strike the fancy of many people.
Interestingly, a similar test is offered to identify red factor carriers in cattle, which are considered to have added value in predominantly black breeds, especially Holsteins. If an owner attempts to register a bay foal out of chestnut parents, the registration authority will ask for verification of color with photographs. If the colors are confirmed as presented on the application, then testing is usually required so that the true parents of the foal can be identified. From traditional studbook studies and the molecular studies on the extension gene by the Swedish research team, we are confident that this test will provide reliable and accurate results. There is the rare possibility that a different mutation causing red might be found, but it is not until we have exceptions to this test that we can work on a test to identify those possibilities.