When I said "small dataset", I should have said "small subset of all collected points that are initially fed to the model". The issue isn't that you have to collect the data little by little. The issue is that, once you've given a linear model an input that is outside the distribution which you're hoping to model, nothing about the model can be trusted.
So you collect all the data points, but you don't give them all to the model at once. (I'm describing the RANSAC method here now) You start with a large number of "candidate models" that are all fit with a small number of input points, and then test which of the candidate models predict well the points you have not yet given the model. Then you feed the best of these candidate models only the points which it predicts well, and create a more refined, still outlier-free model. This can be proven to work in the presence of a small number of out-of-distribution points.