There's a lot of scenarios that could produce what we witness, and eliminating one doesn't prove which of the others it is.
It could be the case that programming talent is bi-modal or multimodal, but each mode is itself a normal distribution. There would be a "talent" involved, but it would still produce a normal distribution once you cut the bottom off. This is suggested by such things as the bimodal distribution on the handful of peer-reviewed papers that at least opened the question about whether incoming freshman could be sorted into "those who could get it" and "those who can't" buckets by a simple multiple choice question at the beginning of the test. (I do not claim they have solved the problem, but it is an interesting data point. This is that paper that was extremely widely misunderstood by professional programmers as being a test that required the students to guess in advance how things like "equality" worked in programming languages, when in fact it wasn't about being "right" about programming languages but about being able to form a consistent theory about how such things might work.)
It may be the case that talent is single-mode normally distributed, but there's also a threshold necessary to function, which can be at any arbitrary point along the curve; I'd suggest evidence would suggest it's certainly above the average as with all due respect to my fellow humans it does not strike me as the case that more than half of the human race can simply become professional programmers. (This is less elitist than it sounds, because in many cases supply & demand is such that only the best can become professionals anyhow, and that's not just "NBA basketball players", it's even things like music composers or painters. If you are a 50%-th percentile composer, do not try to make a career out of it. I say this as one who has faced down this choice personally.) The resulting truncated-normal distribution of talent in the professional space would have a lot of people piled up on the bottom, being just barely able to cross over the talent bar, and then a long-tail effect where extremes would be more likely than you'd naively expect. Further, courtesy of the Central Limit Theorum, as this initially non-normal distribution of talent went through the usual random vagueries of life and professional career, it would be the case that the curve overall would become more normal, but would be quite likely to retain the longer tail and never be quite normal. This is suggested by the fact that this rather does sound like the programming world we live in.
Further if we're going to go all social-engineering on the question, I'm not particularly interested in telling people pretty lies to make them feel good, or worse, make ourselves feel good about how good a person we are, while sucking them in to a career that does not suit them. If talent exists and matters, then it behooves us to say so and give people the ability to examine themselves with eyes open and ask if this is the right thing for them, or if they should pursue another career which they may find more satisfying. There is, of course, a lot of room for "average programmers", almost by definition, and "average programmer" already likely entails "above average talent when the whole population is considered".