Brown recluse spiders live in a well defined area in the southeastern part of the United States. Within their habitat they're hard to find. They are called "recluse" for a reason: they don't like to play with others. These spiders like dark, dingy places. They hide under things and prefer living where the sun don't shine.
Inside their habitat, brown recluse spiders cause serious infestations. Where there is one, there are most likely dozens or even hundreds. However, even in homes with such outrageous infestations, bites are very rare.
The scientific name for the brown recluse is loxosceles reclusa. In all those other colored areas of the map are other loxosceles species (Texan recluse, desert recluse, etc). They're related to the brown recluse and all have similar venom. Indeed, some of the other loxesceles species have worse venom than the brown recluse.
So, if the spider was found outside of the known habitat of a brown recluse, then it is almost certainly not a brown recluse. Outside the other areas means it's not even related to the brown recluse. If you have a specimen from inside the brown recluse zone (or if you think the experts are wrong about your particular spider even though you aren't in brown recluse territory) then let's try to figure out if it's not a brown recluse.
Let's take a look at its legs.