Unlimited freedom is only God's. The forbidden tree served as a reminder that we are not unlimited, but it also meant that we are free within our capacities to make free-will decisions.
Adam and Eve were perfectly free to reject the Serpent's offer. They were not forced to eat the forbidden fruit. They made a free decision to disobey.
It depends on how you look at it. First, I would agree with you that God did not drop a "sin bomb" on Adam and Eve, forcing them to blow it. However, what do you suppose would have happened if they passed the test? Would the serpent have slithered away, defeated, never to return? Or, would he have done what we all know satan does all the time, keep trying? Since we know for a fact that they DID have the potential to sin, unlike Christ, they would have cracked after some amount of time. We know this was by God's design since He could have easily protected them from that potential. But He didn't. So, everything happened exactly as God ordained it. Does that offend their free will to sin? I would say "no".
I for one like the way Harley has described this in the past. I believe, (Harley correct me if I'm wrong), that he has said that Adam and Eve simply didn't have the tools to know what to do here. Eve DOES come off looking like a total ditz and would have been easy pickings for the serpent. God, of course, knew that and allowed it anyway. This is very different from God "inserting" evil into anyone, but it also shows that God's intent was that the Fall happen.
Tsk, tsk. As I've pointed out several times now, Eve did not make a "free decision" to disobey; she was deceived. It states this twice in scriptures. To say Eve made a "free" decision while being deceived is like saying people who are tricked into signing a document made a free decision. I guess we wouldn't need as many lawyers. If it give any comfort, I should point out that I was listening to a sermon this weekend by a well respected Reformed preacher who indicated the same thing. He was wrong as well.
This is a rather important point in understanding the fall of Adam. It was because of Adam that the race died, tainted by original sin (which the Orthodox don't believe); not because of Eve.
There are only two choices; God's way or sin. That's it.