Imagine a timestamp defined as days since January 1, 1970, except that it ignores leap years and says all years have 365 days. Leap days are handled by giving February 29 the same day number as February 28.
If you do basic arithmetic with these timestamps to answer the question, “how many days has it been since Nixon resigned? then you will get the wrong number. You’ll calculate N, but the sun has in fact risen N+13 times since that day.
Same thing with leap seconds. If you calculate the number of seconds since Nixon resigned by subtracting POSIX timestamps, you’ll come up short. The actual time since that event is 20-some seconds more than the value you calculate.
If you have a timestamp defined as days since January 1, 1970: If you do basic arithmetic to answer the question "How many days has it been since Nixon resigned" you will _always get the right number_. There are no leap days, they are just normal days.
The problem only comes in when you try to convert between this date type and other types. Our "days since the epoch" date type is fully internally consistent. As long as you know the correct value for "the day Nixon resigned" and "now", it's just a subtraction.
It works out to be that unix time spits out the same integer for 2 seconds.
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.