Silly question from the UK, but how can you tell. I thought they had a fiddle/violin mark on their back or something , I can't see anything , but then again we don't have them over here.
I am no spider expert as snakes are more my thing. However, brown recluses tend to have several different shades. In this photo, you do not get to see the head very well so you can not see the violin shape. Also, they typically have darker colored legs than their bodies and the abdomen is very defined from the head. This example does not show either of these. Not an expert but my two cents for what it is worth.
If I had glanced down at my detector and saw that alien so close to my hand I would have freaked. The detector would have went flying in one direction and I would have went flying in another. Screaming blindly like a banshee until I tripped, hit my head on a tree and woke up the next day to the search party my kids would've called out.
Cool pic and doesn't look like you're shaking in the pic. Doesn't look like the fiddlebacks I'm familiar with due to the legs and the joint in the body. Could be a northern variation, so remember they're nothin to mess with.