It could explain the issue, but you should get a warning while loading e.g. the module.state_dict() into the nn.DataParallel model.
The reason for this is that the nn.DataParallel(model).state_dict() will add the .module names to each parameter, which will then create a mismatch in the model.load_state_dict() operation (the same applies for the reversed workflow).
However, if no errors were raised, I’m unsure what might have been the root cause of the issue.