That site is helpful in a lot of ways, but it does have to be taken with a grain of salt - it's about 15 years old at this point, and not everything is still applicable.
(Also, although it does say in big letters to never insert at a downward angle... then the instructions add "It may be necessary to put your thumb or finger on the top of the dilator shaft and apply slight pressure so that the nose of the dilator passes under the pubic bone." So my guess is that it's basically a question of how the dilator and personal anatomy is designed; the "never insert downward" warning is to avoid causing a fistula by driving the dilator into the rectum, but it's generally clear to the person doing it when/how to nudge it under the pubic bone - your instincts were good. As you noted, if it doesn't go under the pubic bone it ain't going in, as over that bone is impossible.

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