  A theoretical justification of the empirical surface hopping method for the
laser-driven molecular dynamics is given utilizing the formalism of the exact
factorization of the molecular wavefunction [Abedi et al., PRL $\textbf{105}$,
123002 (2010)] in its quantum-classical limit. Employing an exactly solvable
$\textrm H_2^{\;+}$-like model system, it is shown that the deterministic
classical nuclear motion on a single time-dependent surface in this approach
describes the same physics as stochastic (hopping-induced) motion on several
surfaces, provided Floquet surfaces are applied. Both quantum-classical methods
do describe reasonably well the exact nuclear wavepacket dynamics for extremely
different dissociation scenarios. Hopping schemes using Born-Oppenheimer
surfaces or instantaneous Born-Oppenheimer surfaces fail completely.
