Yes. An elevated PSA does not always indicate the presence of prostate cancer. It is very common for some men to have high PSA and for it to increase with age without any significant abnormality being detected. Some men, on the other hand, simply have high PSA because they have a large prostate.
Therefore, there is no need to be alarmed by an elevated PSA without a clear diagnosis. Even so, it is advisable to perform periodic PSA analyses to observe its evolution over time.