Such a conclusion can be made because spectral observations indicate that SDSS0533 does not have a low surface gravity. This implies that SDSS0533 had sufficient time to contract to its current size, and the same mass in a smaller volume gives a higher surface gravity. Since SDSS0533 is a red dwarf star, it is hot enough to have an L0 spectral type despite its old age. If SDSS0533 is a brown dwarf, it would have already cooled too much to maintain an L0 spectral type.
The white-light flare that erupted on SDSS0533 is one of the strongest detected so far. During the flare, a significant area on the red dwarf star is predicted to have reached temperatures exceeding 10,000 K. For comparison, the normal temperature on such a red dwarf star is only ~2000 K or so. Based on the best-fit model, the flare's luminosity appears to have a half life of approximately 180 seconds. The detection of ASASSN-16AE shows that violent stellar-type activity can occur for objects belonging to the L spectral class. Objects in this spectral class include the least massive stars, and the youngest and/or most massive brown dwarfs.
Schmidt et al. (2016), "ASASSN-16ae: A Powerful White-Light Flare on an Early-L Dwarf", arXiv:1605.04313 [astro-ph.SR]