Actually, both of you are right. Japan does have a lottery, but they also accommodate most (if not all) entrants.
Let's use Tokyo for example. From last year's attendance, The Pokemon Company decided to hold three tournaments in Tokyo, spaced months apart, to accommodate last year's capacity crowd. Interested participants choose one of the three (although the window for registration is different for all three so that those who miss the first can still attend the second or third after discovering they were not selected for the first), and submit their desire to participate online, months in advance, during a month-long window. After the window closes, the company rounds down to the next power of two. To keep the bracket symmetric, the company rounds this way so that nobody earns a "bye" or some other unfair advantage.
The first Tokyo event had 1024 entrants. Of course, rounding down means that as many as 1023 entrants missed out, but they discovered this without actually attending, months in advance. In other words, once they knew they were not selected, then they could sign up for the next Tokyo tournament, which occurs two months after the first. As a result, many who failed to either submit during the first window, or who submitted and were not selected, could try again. Using this method, only those who are rounded out during the final window (for the third Tokyo tournament) failed to play.
People could not take advantage of this method by traveling because the Pokemon Daisuke Club (which does not mean Love Club, exactly - it's more of a fondness) tracks mailing address, so players cannot attend remote tournaments, and, once you register for one, you are handicapped in the next lottery (in other words, you have low priority on the wait list). Still, selection for your first entry stands up well, because the lottery rounds down to the nearest power of two, and, in the small chance you are rounded out, you could rely on last year's statistics convincing the company to hold a second qualifier there, months later. In the end, they have two Last Chance Qualifiers, open to everybody, in West and East, for people who either lost (and want a second shot) or for those who were rounded out in the final tournament in the prefecture.
In summary, there is a lottery. However, they make every effort for all to participate, so they determine the cap only after receiving all entries online. Afterwards, lottery determines which of the 128, 256, 512, 1024, 2048, ... to accept, and people who are not selected then can sign up for the next tournament two months before that one, again online. You are notified quickly enough of your non-selection that you do not need to commit travel, and can still make the next window in your prefecture, if you live in a large one like Tokyo's or Kanagawa's.