"Heterozygous" essentially means carrying just one gene for a recessive trait. Since the animal only has one gene, it doesn't express the trait.
That is not what heterozygous means. Heterozygous means that an organism possesses non-matching alleles at a given locus. Whether an allele is recessive or not is irrelevant to the discussion of heterozygosity.
Your definition works in a few cases where we are dealing with a pair of alleles where one shows dominance, but it doesn't explain heterozygosity in all the other instances it can occur. What about heterozygosity in codominant traits?
I know you were trying to simplify, but I think there is a loss of information in oversimplification and that such a loss of information can lead to misunderstanding.
For example, trying to understand heterozygosity without understanding diploidy and syngamy makes no sense at all and is more confusing than if you just learn all the background information. I think that oldherpers glossary is great, but if anything, it could provide MORE detailed explanations rather than less detail.
We use all sorts of shortcuts in the vernacular of this hobby, but I think it is better for people starting out to try and learn it correctly, so they don't have to relearn it later.
In case I sound like an old nag, don't worry. The fall semester starts in two weeks and I will have a classroom full of fresh young nursing students to nag instead of you guys. 
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Chris Harrison
San Antonio, Texas