The propagation of a free scalar field φ with mass m in a curved background is generally described by the equation (9μν ∇μ ∇ν + m2 + ξR)φ = 0. There exist some arguments in the literature that seem to favor the conformal coupling to the detriment of the minimal one. However, the majority of these claims are inconclusive. Here we show that the exact Foldy-Wouthuysen transformation for spin-0 particle coupled to a wide class of static spacetime metrics exists independently of the value of ξ. Nevertheless, if the coupling is of the conformal type, the gravitational Darwin-like term has an uncomplicated structure and it is proportional to the corresponding term in the fermionic case. In addition, an independent computation of this term, which has its origin in the zitterbewegung fluctuation of the boson's position with the mean square ((δr)2) ≈ 1/M2, gives a result that coincides with that obtained using the aforementioned exact transformation with ξ = 1/6.