Yes, I think it is fair to say that if you think QM is "just an algorithm" you must also be similarly open minded about the very existence of particles like electrons, quarks etc. We can't directly detect them. All that we can directly observe are the states of macroscopic measurement devices.
So, if I play the Devil's advocate, I could claim that Nature is described by a fundamental theory that one can turn into an effective theory yielding statistical predictions using a path integral formalism involving integrating over fictitious field configuarations.
The formalism is then the same as the Standard Model, except for the fact that only the sources and sinks of particles are real, not the particles themselves. So, when you compute amplitudes for process using Feynman diagrams, the external lines always start end end at detectors/sources. The amplitude is associated to the state of the detectors, not to particle states.