I wonder if the author is right; using a slightly wrong capacitor for the clock (keeping in mind that they're usually +/- 10% or worse from the factory) may produce a different oscillation speed, but usually not an outright failure. These chips accept a pretty wide range of clock frequencies.

And in the comments, they note:

"I replaced the 18pF capacitors on one of the non-working boards with 10pF capacitors, but it still doesn’t boot or respond to the debugger. That surprised me – I thought that was the answer! It was a rush rework job and I made a bit of a mess of it, including accidentally desoldering and reinstalling the crystal, so I’ll try again later with another board. But it appears that the capacitor value may not have been the issue after all. Either 10pF is a bad value, or it’s the crystal itself that’s at fault, or I’ve failed somewhere in my troubleshooting reasoning. Hmm."

In my experience, mystery stability problems are often caused by capacitors, but of a different kind: decoupling capacitors on the power supply pins. If there's not enough of them to keep up with the noise originating from motors or digital switching, I'd expect that exact issue. Intermittent "impossible" CPU states on some boards, no rhyme or reason (because sometimes, that +/- 10% saves you and sometimes it does not). I'd try more caps and possibly some ferrite beads.