However, after looking hard at the tables in that Wikipedia article comparing TAI, UTC, and Unix time, I think you might actually be correct-- TAI is the atomic time (that counts "real seconds that actually happened"), and it gets out of sync with "observed solar time." The leap seconds are added into UTC, but ultimately ignored in Unix time.* ~~So Unix time is actually more accurate to "real time" as measured atomically than solar UTC is.~~

The only point of debate is that most people consider UTC to be "real time," but that's physically not the case in terms of "seconds that actually happened." It's only the case in terms of "the second that high noon hits." (For anyone wondering, we can't simply fix this by redefining a second to be an actual 24/60/60 division of a day because our orbit is apparently irregular and generally slowing down over time, which is why UTC has to use leap seconds in order to maintain our social construct of "noon == sun at the highest point" while our atomic clocks are able to measure time that's actually passed.)

*Edit: Or maybe my initial intuition was right. The table does show that one Unix timestamp ends up representing two TAI (real) timestamps. UTC inserts an extra second, while Unix time repeats a second, to handle the same phenomenon. The table is bolded weirdly (and I'm assuming it's correct while it may not be); and beyond that, I'm not sure if this confusion is actually the topic of conversation in the article, or if it's just too late in the night to be pondering this.