Well, it is close enough. The definition is that a brown dwarf forms like a star through gravitational collapse within a protostellar nebula, but it just wasn't massive enough to ignite. However, a planet forms in an accretion disk around a star that is forming out of the larger cloud. Of course, nature does not always perfectly align itself within our neat categories, and it is not really possible to distinguish between a brown dwarf and a supermassive planet that happened to be ejected from its star. Anyway, perhaps such a supermassive planet that is not ejected should really be considered a brown dwarf in a binary with the "parent" star. For gravitational collapse to occur in the first place, however, requires a minimum density which sort of puts a lower limit on the mass of a brown dwarf, so smaller objects are not really going to form independent of an accretion disk, but they may form in one and be ejected as you say. So yes, there is kind of a practical line between planet and brown dwarf, but it is a bit of a fuzzy line.