There doesn't seem to be much differences between GISTIC 1.0 and 2.0 as it says:
As with GISTIC 1.0, we obtain P-values for each marker by comparing the score at each locus to a background score distribution generated by random permutation of the marker locations in each sample
But on the supplementary material of the GISTIC 1.0 there is a more detailed explanation of the method. See the "Stage 2" section:
Second, we compare these G-scores to the distribution of scores expected if only random aberrations were observed. This distribution can be determined by rescoring the genome after permuting marker locations within each sample; we instead derive a semiexact estimate.
Furthermore in another section ("Stage 2: Aggregation of Data from Different Tumors to Differentiate Between Driver and Passenger Aberrations") it says:
To determine which of the aberrations identified in Stage 1 are likely to represent driver events, we aggregate the data from all tumors used in the analysis to generate summary scores for amplifications, deletions, and LOH. The statistical significance of each score is determined by comparison to the distribution of scores obtained by all permutations of the data (using a semiexact approximation), with correction for multiple hypothesis testing.
However, the relevant section (of the supplementary materials) seems to be "Null Hypothesis Generation: An Analytic Derivation of the Null Distribution", where it describes the semiexact approximation used.
In a supplementary file it describes it as "Generate all permutations of SNP labels within each sample to simulate datasets with random aberrations"
Conclusion:
It seems that the background probabilities are calculated within sample.
I can't say if it matters how the sets are constituted but I would say that the broader the sets are, the better estimation of the structural variations it will perform but the same estimation of the background will be done.
Ultimately you can check the code of the program, or test with 10 samples and replace one of them to see if the results are changing accordingly.