Also from the page you refer to is:
At newly public companies, grants made before the initial public offering (IPO) may also require a liquidity event (i.e., the IPO itself) to occur before the shares vest. Once the liquidity event has occurred, the shares vest 180 days later.
So, combined with the quote you gave, unless the terms of the RSU specify otherwise:
Event 1: You are granted some RSUs.
Event 2: Your company has its IPO: the "liquidity event".
Event 3: Your RSUs vest and become taxable (180 days after Event 2).
And to clarify:
But I'm pretty sure I haven't been taxes on RSUs I've received from a pre-IPO company, so I suspect it's not always when the shares are delivered. Or are they not considered delivered until they become liquid (e.g. IPO)?
Receiving RSUs is not the equivalent of "when shares are delivered". In effect, RSUs are a promise to receive shares at some future time (according to the vesting schedule). In the case of pre-IPO RSUs, then both the shares have to exist (i.e. the IPO has to have happened) and the RSUs must have vested (the promise is fulfilled by receiving real shares) before they become taxable.