I think you may be confusing the event horizon with the Roche limit. The event horizon is the distance where not even light can escape. The Roche limit is the closest a body can come to another (more massive) body such that it can stay intact with itself, as opposed to being torn apart by tidal forces in the massive object's gravitational field.
I suspect, but do not know for sure, that the Roche radius for a black hole and regular star is much larger than the event horizon for the same black hole.
They are actually somewhat independent. The Roche limit depends on both body's mass and volume, where the event horizon relates to a single body mass and volume.
EX: Cold Brown dwarfs can orbit closer together than a brown dwarf and a earth like planet.
PS: Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Jupiter's moon Metis and Saturn's moon Pan are examples of such satellites, which hold together because of their tensile strength.
Interestingly the equation for the Roche limit has a term for the radius of the primary, but not the satellite. Only the density of the latter matters, not its size.
Basically correct (except the concept of volume doesn't hold up in a black hole). It is theoretically possible to have a black hole big enough that its Roche limit is inside its event horizon; but a black hole that big is probably at least vanishingly rare in the observable universe.
A black hole has a volume less than it's event horizon. So, it's not really undefined as much as ill defined. Also, a black hole's event horizon is not necessarily a perfect sphere ex: two black hole's orbiting each other.
And yes, some quick Googling turns up several papers that talk about the Roche limit for a black hole and a star being well outside the black hole's event horizon.
I suspect, but do not know for sure, that the Roche radius for a black hole and regular star is much larger than the event horizon for the same black hole.