FU Ori-type objects (FUors) are characterized by short (decades- or centuries-long) episodic accretion bursts, during which their luminosity increases by orders of magnitude. A possible cause of such events is gravitational interaction between encountering stars and their disks. Numerical simulations show that this scenario requires a close approach of several to several tens of au to reproduce relatively short, year-scale, characteristic times of luminosity rise via the release of gravitational energy. However, objects in FUor binaries (including FU Orionis itself) are usually hundreds of au away from each other. Then, relative velocities of sources, which can be estimated from the known burst duration timescales, should have been by at least an order of magnitude higher than the observed velocity dispersion in young stellar clusters. Thus, the burst onset either has a delay after the closest approach or bursts should be initiated due to a mechanism that is different from a direct gravitational mass and angular momentum exchange during a close encounter. We used numerical hydrodynamic simulations to model the possible mechanisms of luminosity burst development during the encounter between a star plus a disk system and a diskless intruder star perturbing the target system. It was found that the encounter can lead to accretion bursts even in models having a large periastron distance ( ≃ 500 au) between the intruder and the target. The delay between the closest approach and the burst onset is more than 4000 years. The target disk perturbation caused by the intruder flyby resulted in the development of magneto-rotational instability in the innermost parts of the disk. This mechanism can resolve the problem of coplanar FUor binaries having large distance between the companions.