Like native plants, weeds have a range of fire responses. They may be killed by fire and need to regrow from seed or are able to resprout from protected buds.
Response depends on fire intensity. In my experience a hot wildfire can kill a lot of Lantana but a prescribed burn is unlikely to be hot enough and resprouting is likely.
A fire needs to be hot enough to kill the obligate seeders and stimulate germination of seed banks.
Some good work has been done in the Blue Mountains treating Broom and Gorse seedlings in fairly remote areas after bush fire. The fire caused nearly all the seed bank to germinate and post fire control removed most of the seedlings before further seed production. The same fire killed large numbers of Radiata Pine trees and wildlings in an abandoned plantation. Follow up treatment of survivors and seedlings has dramatically reduced pine abundance.
But the herbivore and competition issues Judy raises are important. Weed control needs to be delayed until it is possible to work in the area without destroying too many native seedlings and most of the weeds are visible and identifiable. The appropriate timing is very site specific so monitoring of recovery after fire and acting at the right time is critical.