Yeah, it usually used to indicate unwanted flowering, but in lettuces (and to a lesser extent, basil) it indicates the beginning of the flowering attempt by the plant. Most people will cull their lettuce after it bolts (stem starts to elongate into an inflorescence), but way before there are any open flowers or even buds.

Broccoli is weird though. We want it to bolt, but not really flower. That’s an odd thing for most plants.

Not exactly. It is bolting when it starts sending up a flowering stem, the very beginning of flowering. Every broccoli I’ve ever eaten has bolted, but not many of them have bolted and flowered.