Possible but theoretically, BDNF should express ubiquitous though out brain tissue. However, I need to confirm the IHC picture to make sure it is not false positive.
You do not mention which anti-BDNF antibody you are using, so I can't comment on your results. However, since BDNF and its pro-peptide are are transported and secreted by neurons, it can be very challenging to determine the subcellular localization of the protein. This challenge has been addressed with a variety of techniques by others in the field. Please see this article from Y-A Barde's group regarding subcellular localization in mouse brain, as well as the references therein: