I hope to help you today regarding your trespassing issue.
To begin with, Georgia's trespassing law is found at O.C.G.A 16-7-21. The statute is found here http://law.onecle.com/georgia/16/16-7-21.html
My question to you here would be to the exact subsection you were cited under on your ticket. As you can see, the law contains three portions. These are subsections a, b an c (subsection c being inapplicable in this case).
Subsection (a) creates a trespass if you intentionally damage the property of an owner without their consent and the damage is less th $500. The key word here is intentionally. If this is the subsection you were charged under, then based on what you have told me, you would have a valid defense as you had a good faith belief that the tree was lawfully on your portion of the land.
Subsection (b) creates trespassing when you:
1) Enter onto someone's land for an unlawful purpose; OR
2) Enter onto someone's land after you had received notice from the owner that such entry was not allowed; OR
3) Remain on someone's land after they have told you to leave.
It appears if you were charged under subsection (b), you would still be able to defeat the ticket. This is because if you were charged for (b)(1) as described above, it doesn't appear that the purpose you entered his land (attaching a climbing type stand) is unlawful. If charged under (b)(2), unless you had received notice from this person not to enter his land, that charge will not stick either. Finally, for b(3), it does not look like he told you, while you were on his land, that he wanted you to leave. So this portion does not apply.
So, in answer to your question, no. I do not thing the ranger was lying to you initially because it appears that, although you believed otherwise, that tree is in the adjoining owner's land. However, since NOW you know that the tree is not on your land, you must remove the climbing stand. So while I believe you may win the current ticket you have based on the above discussion, your failure to comply with the removal request may subject you to a separate ticket, and this separate ticket will give you more problems as you now have knowledge of the owner's land delineation and notice that you are to remove the climbing stand.
I hope this answers your question. Feel free to respond back with any follow ups. If you do not have any further questions, please leave a positive feedback so I may receive credit for my response.