By the term "archaeology" I mean to say "material culture" apart from the texts that are found by archaeology. Here's my basic argument.
Liberal historians of ancient Israel currently employ a methodology of skepticism toward the Bible's record of history. Anything that is not proven by either material culture or extrabiblical texts is doubted. In many cases, material culture is interpreted in such a way as to contradict the biblical text. It would be interpreted to contradict the biblical text en toto, but extrabiblical texts have helped support the existence of these events and people more often than not. But herein lies the problem.
It is clear that when extrabiblical texts are removed from verifying biblical history in some way, the material culture is almost always interpreted in a way that contradicts the biblical history. So when historians talk about the patriarchal period, the exodus, the conquest, etc., since we have no texts, other than the Bible, that support this history, the material culture is used to say that these things did not happen in the way the Bible describes. In fact, the very existence of the events and people is called into question.
But this was/is also true for those people and events when only current skeptical theories using the material culture was applied apart from extrabiblical data that proved otherwise. Before Tel Dan, many scholars who applied this methodology did not believe in a united monarchy or in the person of David. Some minimalists still believe the concept of an Israelite nation was made up by Jews in the Persian period, and they interpret the material culture accordingly. This methodology thus verifies for them that there was no historical Israel before the exile.
The problem is that when we actually have texts, i.e., things that speak and can tell us if we are wrong about the existence of certain events and people, they contradict this conclusion.
So here is my argument. If the texts contradict the conclusions of the current methodology of inquiry, and the texts are more reliable than contemporary theories and guesses about potherds and burn layers, then the conclusions brought about from that particular methodology are wrong even in the periods dealing with people and events where we don't have extrabiblical texts informing us of their errors.
Now, that doesn't mean that all of the biblical persons and events are proven to exist. It just means that the current methodology and ideology has no way of figuring that out apart from text. Hence, we are back to the oldest extant text commenting on those persons and events, and that would be the Bible in many cases. It contradicts an obviously flawed methodology, and I have no reason, therefore, to reject it based on the conclusions of that obviously wrong methodology.
To put it plainly. When X concludes Y, but Y is shown to be false by Z, then when X concludes Y, and Z is not present, there is no warrant to trust X.