In my view that would have to be flipping bits randomly (flip/no-flip). By flipping every bit you are creating a (anti-)correlation. That would be similar to the correlation an entanglement would yield. The fact that there is a correlation is what sets this kind of 'randomness' apart from the example with two independent sources. If you compare two 'truly' random ('independent') strings, you won't get a correlation in any aligment. The strings from a source like an entanglement experiment that have a correlation only yield a correlation when the strings are aligned absolutely. In any other alignment they are random (p=0.5). It is the correlation that sets correlating bitstrings apart from, in my definition, 'true' random bitstrings.That definition doesn't work. A trivial counterexample would be the string S' that I get by flipping every bit in a random string S; S' is no less random than S itself (all I'm doing is changing the symbols that represent the string), yet there is a 100% anticorrelation between the two.
Entanglement data and artificially generated correlations (like in my code) are identical with respect to my argument. It is just that correlating data is random in every other alignment. That would be random, were it not that in exactly one alignment they correlate. This differs from independent random sources. It is this difference that sets correlating data apart, in my view.
Correlation is, as it were, a 'hidden payload'.