Bias is not a boolean quantity. The underlying data set is somewhat biased, and the "trick" being used greatly exaggerates the impact of that bias.
And bias can certainly be of different magnitude. A weighted dice can have a bias that shows up after only 10 rolls and another one can only show it's bias after 1000.
A random sample is not a product of a biased sampling method, but it can be (and almost always is) biased, it's just if you take enough such samples, the biases will tend to offset, which is why we say the sampling method isn't biased.