Yes.
The following explanation is no doubt over-simplified or wrong. I read about population genetics in a Pop Sci kind of way. I hope those among us with modern training will correct me.
Think of SI as a self-fertilization-death-to-inbred-offspring gene. Self-incompatibility seems to be a process by which one precise allele - a form of a gene that must have many, different, variable forms within the population of the species - triggers a growth process that aborts the normal reproduction. [SI is more likely a complex of genes, but this will work for now.]
Stated another way, self-incompatibility is stored in an SI.a-form of a gene in a single plant. When a plant’s own pollen pollinates the pistils, the SI mechanism is activated, and the reproductive process is aborted: death to the potentially inbred offspring. The same gene, but without that specific SI.a-allele, is carried by other (but not all) Rosa multiflora plants. Pollination by plants without the specific SI-allele and instead carrying SI.b, SI.c, SI.d or SI.e…z-alleles (or even lacking any SI-allele!) results in normal reproduction.
In practice, you can pollinate with another plants (not another clone) of Rosa multiflora, and, depending on how many different SI-alleles exist, you’ll get a successful pollination that isn’t a hybrid. Note I didn’t say “pure” multiflora, but that’s how we think of it. Rosa multiflora is a population of individuals. Certain members of the population are going to have that particular SI.a-allele and the pollinations by those members are going to fail. Other individuals will have SI.b, SI.c, SI.d, etc. alleles, and pollinations by those members are going to succeed. The success rate will depend on how many different alleles exist among the available pollinators.
I don’t know if the research is clear how this system works in Rosa, let alone in R. multiflora. Maybe there are 4 or 20 different SI-alleles. Google gametophytic self incompatibility, and you’ll get many hits explaining hypotheses with nice graphs.
This is a favorable evolutionary strategy for a species with a large population in which there is no shortage of pollinators from diverse members of the population. It prevents inbreeding and promotes diversity. And as the Debener article shows, Rosa multiflora “recruits” pollen from other compatible roses when an appropriate mating doesn’t occur. One hypothesis in the invasive plants research is that resulting hybrids then back-cross into the species, contributing another form of the SI-allele, allowing pollination to recur from within the population.
Population bottlenecks and the Founder Effect are other population genetics theories that explain our inability to produce representative species roses when the only plants available for breeding are either clones or seedlings from a single hip.