Looks like there's some nuance here. From your linked document (emphasis mine):

> Although Congress has ultimate authority over federal lands under the Property Clause, states have legal authority to manage federal lands within their borders to the extent that Congress has chosen to give them such authority.

So whether California is able to manage forests on federal land within state borders to address the risk of uncontrolled fires isn't immediately clear, and presumably someone would need to dig up a relevant statute, if any, to show who is actually responsible.

They have the authority, but do they have the duty?

Also, "could" doesn't mean that they do. From your very own link:

"States can obtain authority to own and manage federal lands within their borders only by federal, not state, law. Congress’s broad authority over federal lands includes the authority to dispose of lands, and Congress can choose to transfer ownership of federal land to states. States have legal authority to manage federal lands within their borders to the extent Congress has given them such authority. As an example, Congress has to a large extent allowed states to exercise management authority over wildlife as a traditional area of state concern. Congress could give states authority to manage certain other activities, resources, or other aspects of federal lands. Congress also could give federal agencies authority to delegate or assign responsibility for aspects of federal land management to states or other partners."