It is true that (at least above the level of quantum physics) we tend to believe that reality is deterministic. When the meteorologist gives a chance of rain, in truth if they had perfect forward information on all of the clouds and pressure systems, they would simply declare whether or not there was future rain. In cases like physical phenomenon, you can think of observed uncertainty or chance as being a product of the exact settings of the unmodeled but deterministic factors underlying a particular outcome, or else errors in the functional form of the model with respect to the measure. We tend to assume that unmodeled factors are as-if orthogonal to the causes we are interested in modelling, and thus zero-centered, and our models minimize error predicated on this assumption.

In your proposed flipping model, there are likely to be very small physical imprecisions (vibrations in the flipper, say, drifting tension of some kind of spring or actuator, or small amounts of circulating air, or perhaps tiny imprecisions in the way the coin is loaded into a slot). The machine might always flip heads, but it's still possible to say that whatever arbitrary degree of certainty you need to model the coin's behaviour in the air to achieve 100% accuracy, there could still be arbitrarily smaller error below that threshold, and we'd view this as "randomness" even if it isn't by the laws of physics.