Sure but we don’t prove negatives for a reason - it’s impossible. We assume the null hypothesis.

LNT is the null hypothesis. No one disagrees a linear model fits the data very well in high doses. If you want to argue that model doesn't work in low doses, you need a model with more parameters and sufficient data to fit it. The issue is that, at these low doses we want to differentiate, we're also looking at effect sizes that are hard to separate from noise, and sampling biases that are hard to erase. There's still lively and ongoing debate.