The blackspot fungus's physical form isn't limited to the spore stage, which explains how the fungus can survive over winter and release new spores in the spring. The technical explanation (which might make one's eyes roll into the back of their head) is this: Once a rose loses its infected leaves in the autumn and they fall to the ground, the fungus's hyphae will invade the dead leaf tissue and form what is known as pycnidia that are lined with conidiophores located under old acervuli (this refers to the fruiting bodies of fungi). The pycnidia then overwinter in the lesions of infected tissue and subsequently burst in the spring, releasing their conidia (spores). Individual spores can live two to four weeks, even after drying out.
This is why it's important to clean up fallen infected leaves in the fall. But even if one does this, there will inevitably be leaf particles left behind. But if you add new mulch on top of these in the spring, the spores released by them won't reach the rose leaves above them due to the mulch's physical barrier.
One other thing... it doesn't serve a viable purpose to use contact foliar fungicides like Actinovate as a root drench (a use that was mentioned above), because these fungicides do not act as systemics. Any uptake by the roots doesn't benefit the leaves' ability to fight infection. Instead, fungicides like Actinovate are designed to kill blackspot on contact, as a leaf spray only.
Ultimately, no matter how much one tries to control blackspot spores on the ground, it will never stop their other mode of transportation, which is through the air. This is why a preventive foliar spray is the best approach in my opinion. It is much easier to prevent Blackspot from taking hold than it is to eradicate it after infections take place.