The study uses a repeated measures design. Per session 10 true and 10 false trials were performed and NIRS was measured using 20 channels over 93 time points. For Patient B there were 44 session leading to a total of 440 true and 440 false trials.
The repeated factors are time, and when doing a combined analysis also channel, whereas the trials are the independent replications of the experiment within a patient. Instead of an ANOVA for repeated measures a simple t-test can be used to test the true/false effect in using the mean over time within a channel for a single trial, or in using the mean over all channels and times for a single trial, when channels are of no interest.
It is therefore not a question of the ordering when building means, but a problem to identify the repeated effect and the replicate.

Example
Let’s assume there are 2 groups each with 3 cases, and each case is observed for 7 days. Each case is an independent replication and time (days) is the repeated effect. When comparing the groups, one may use the mean over all 7 days per case. It wouldn’t make sense however, to use the mean per day for group comparisons. In doing so the wrong sum of squares would be used. Let’s assume there is no day effect and no group effect. When using means per day within each group, variability within each group will be very low as this is the mean day effect which is zero. Hence, although there is no group difference, it is possible to detect one due to the wrong sum of square.

Finally, when using data for patient B one can see, that in about half of the trials the true signal is below the false signal and in half of trials it is above. So there is no difference between the true/false tests.