,remote forces are usually used when two bodies are welded or if you are cutting a body from somewhere and then putting a part of it into your model (there might be several reasons for doing this, for example the part which you are not including is not experiencing too much stress according to your judgement even before conducting the analysis, this part might not be the critical region of study for stresses/strains/displacements, etc).
Assume you are just attaching the rubber band at the pins and pins are bolted or bonded onto the bodies. However, the connection between the pin and rubber band is not a weld neither is a continous body which you can cut. What I am trying to say here is that if the rubber band for example is pulled perpendicularly (w.r.t to its length direction) then the bodies won't be experiencing any internal forces or stresses, however if you try to model this case as a remote force, the two bodies in Ansys will. If the band was also welded onto the pins and then you try to move it up, then and only then the two bodies will also experience the internal forces and stresses. (Well, I am here assuming that the pins are straight without any hook at the top). This is when you can use a remote force in Ansys. Moreover, even if you weld the bands onto the pins, and then try to pull it, the band is a hyperelastic material, meaning that it will deform alot before it starts transferring any forces/moments onto the bodies. If you try to model this case inside Ansys using remote forces, it will not be correct since the remote force doesn't know how much the band has already deflected before it starts transferring forces and moment onto the bodies. These two are separate things and will result in different answers i.e. you will observe a difference in results in reality and in Ansys.