If you're just spraying a thin coat onto the foam board, there shouldn't be a problem with using water-based finishes. The problems that people have had come about when the surface of the foam board is flooded with finish. The water penetrates the paper, causing it to expand. This expansion can warp the model or cause the paper to detach from the foam.
To use a wood analogy, applying a finish to foam board with a brush is analogous to immersing a piece of wood with the same finish for an extended period of time. You can apply water-based Minwax to a sheet of wood without causing any warping. But if you were to soak the wood overnight in any water-based finish, the wood fibers would expand, and the wood would warp. You can soak a piece of wood in oil-based varnish and it won't warp, because the fibers in the wood don't expand when they absorb the solvents in the varnish.