You don't, and it doesn't matter. But Broussard's arguments get nowhere at all.
The big problem with Broussard's argument is that he fails to consider the distinction between what might be called ‘natural’ and ‘supernatural’ errors of perception (reflecting Carrier's definition of ‘supernatural’ as referring to the irreducibly mental).
To illustrate, suppose I look at some lines, and observe that some of them look longer than others; but then I take a ruler, and see that they are the same length. This is a ‘natural’ error, since it is explained by the way that the visual cortex is wired. But now suppose that when I read the ruler, I see different numbers of marks according to which line I'm measuring; are the lines really different lengths, or is something interfering with my perception of the ruler as well? What if I substitute a ruler with different units, or a digital caliper? Or get two different people to measure one line each and tell me the lengths? If something is messing with my perceptions in an inherently mindlike way, then it is capable of systematically altering all of those results in order to deceive me.
Descartes has the right idea in imagining his deceiver as being a mind—but he had no true conception of how far the deception could really be taken.
(A related argument to this one also applies to the ‘brain as a radio’ argument for dualism; if the brain is only a communicator, then a damaged brain should only be able to distort the message of the immaterial mind in non-mindlike ways, which turns out not to be the case.)
To the metaphysical naturalist, this is all no problem at all. The ‘natural’ errors of the senses are handled by ordinary scientific methods. The hypothesis of a ‘supernatural’ deceiving demon is sufficiently implausible that it can be neglected. Arguably, though, the theist has no such defense.
The danger, of course, is when arguments against the ‘supernatural’ deceiver are used to argue against the natural errors and biases of our perceptions and cognition.