Group Analysis on time series data

The paper about Canonical ICA for group titled : “A group model for stable multi-subject ICA on fMRI datasets” says that the data is concatenated along the time axis for group analysis.
I am not clear as to how a normal concatenation helps in creating groups. Mere concatenation may even be considered as single subject data with varying signals in the time series. Isn’t it.
Can someone give a crisp and clear reason for the same?

Which specific part of the paper are you referring to?

The data are concatenated along the time axis, but only after a first level modeling with an SVD. This step is what accounts for the variance specific to the subject, and thus creates a group level.

The content in the paper says: Different strategies have
been adopted for group-level extraction of ICA patterns. Patterns
estimated at the subject level can be merged to form group maps although this is a
challenging task because the correspondence of individual maps may
be hard to assess and the merging operation is difficult to model from
a statistical point of view. Individual-subject volumes can be
concatenated along the time axis to apply the ICA algorithm on the
group data.
I am still not clear as to why is it valid to concatenate along time axis to generate a group level data.

I believe that this sentence is extracted from the introduction, and describes other strategies, not what we do in CanICA.

Such a concatenation is a “ConcatICA” strategy, as implemented in Melodic or in the GroupICA toolbox. It corresponds to a model that the time-points are drawn iid across subjects.

Ok. I have seen data being concatenated this way in many group level algorithms and just wanted to know how does this makes sense. Is it that the data is independent and identically distributed thus even after concatenation maintains individual subject property too for further group analysis?