The usual (f)MRI image consists of some low-intensity background, and the default threshold works well to exclude this background from analysis plus some of the voxels "outside the brain" which result from smoothing the raw image. The default setting might be problematic if you encounter B1 inhomogenities (e.g. common with multi-channel coils -> lower intensity with increasing distance from the coil elements). In that case lowering the threshold ensures that you include these voxels / regions, but this doesn't solve the issue with noise. Alternatively, and maybe more elegant, you could go with a bias-corrected version of the (smoothed, normalised) mean EPI image which should eliminate some of the intensity differences. Bias-corrected versions can be obtained via the segmentation routine, and the image could then be thresholded manually according to your needs.
The default threshold only takes into account intensity, and low intensity doesn't mean noise per se, but probably, it's not just lower intensity, but worse SNR and/or CNR. If you want to rely on a region with low intensity you should thus ensure you have a (reasonably) good SNR/CNR (see e.g. Welvaert & Rosseel, 2013, PLOS ONE, http://dx.doi.org/10.1371%2Fjournal.pone.0077089 to get an overview) and optimize the sequence if necessary, otherwise the analysis won't make much sense = searching for voxels that correlate with noise.
Hope this helps a little