Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In this paper, we show how a special form of this concept can be used to devise a variant of the L-shaped method that integrates the advantages of the traditional variants while avoiding their disadvantages. On a set of 104 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that significant speed-ups in computation time can be achieved by applying the concept of on-demand accuracy.