For any experimental science, the integrity of experiment (thus reliability of data) is important. For experiments with human subjects, the question is whether the subjects answered the questions in good faith. A sequence like 'HHHHHHHHHH' for the coin toss experiment looks like an answer in bad faith; it is mechanically easy to keep pressing the same button, and a subject is unlikely to think that such a sequence is a likely random sequence. Therefore, the replicating authors are fully justified to eliminate those poor faith answers. The original paper authors' claim that 'HHHHHHHHHH' is as equally probabilistic as any other sequence is irrelevant.
Edited for clarity.