I expected a little blurring yeah but the strange thing is that some images are noticeably more blurred than others when there is no rotation or scale being applied and positions are at whole integer values.
Your tree definitely looks much better with linear filtering however my stuff generally comes out better with the point filtering on at the moment so I'm very glad Nate was able to point that out to me. There are some slight artefacts on the arms when I rotate them but it's not too bad.
I am indeed using the texture packer built into Spine and have tried toggling the power of two and square options to check to see if this makes any difference, unfortunately it doesn't.
I don't think the issue lies with the texture atlas itself but rather the shape of the cropped texture, polygon and UV layout that's used when drawing the spine elements. It so far seems that by using a square aspect ratio source image this improves the linear filtering at run-time because the polygon being drawn is of a square aspect ratio, though I would need to conduct more research to make a concrete judgement on that.
I've attached an example to show how it ends up looking:
The first character is the art in Spine, as you can see the torso and head is slightly more blurred than the rest and doesn't sit too well, funnily enough the legs at that point are a square aspect ratio so they are sharper.
The second row of characters is in-game with linear filtering, the guy on the right looks tip top but the left ones legs and torso suffers from the blurring.
The final row is with point filtering, everything looks nice and sharp.