I think that is a great idea too. If the PSA blood sample can be taken along with some other blood test, so much the better.
In my case, the first problems showed in the PSA tests, not the DREs. So from my perspective, it makes good sense to follow up high PSA with a doctor's visit and DRE, which is a very minor procedure compared to what most of us here has been through. But I can appreciate the reluctance!
Maybe the medical center is concerned about false positives -- high PSA and no cancer -- and there certainly would be a fair proportion of those.