Not the same.
First, your analogy looks at sin as mere confusion - not the evil act of will that it is.
Second, God is not a fireman. A fireman is obligated to fight fires. You can not obligate God to do anything. He is God. He will be consistent with His justice and holiness and will show mercy as He wills and will give grace as He wills, but He is not obligated to give His creatures any more than He has already given them. In fact, He isn't obligated to do anything for them. He is the potter. They are the clay. If He wishes to destroy all in the fire, He can do so. The fact that He doesn't is pure mercy.
But even at that, even if a fireman were a good analogy of GOd, you havent' given the correct view of the fireman. You see, the fireman not only cleared a path for escape accessible to all, but put His very life on the line and offered to stand in the fire for them if they would just leave. All they had to do was enter the path that He prepared. Yet, they refused. In fact, they hated the fireman. They loved the fire. They would rather burn than turn towards the fireman. They spit upon the very gift He gave them and ignore His path instead deciding to pursue their own path.
True, the Fireman has the power to save everyone in the room yet the more He reaches towards the people the further they run.
He is just in allowing all to burn. But in order for others to see the consequences (Which they never could without His allowing some of the consequences to play out); He chooses to save some of them while allowing the others to follow their desired course.
I can't for the life of me see the difference. They are born that way. Can be no other - unless you pick them. It doesn't matter that they love the fire - they can be no different in your view. They absolutely never had a chance from birth on.
Can't you see this point?
You say they have no choice, now they have a choice? Which is it? Can they choose to not love the fire without your intervention?
Isn't your whole structure based on no choice?
Or as you put it earlier: How can they be free when they are bound by sin?
Why "allow them to see the consequences?" They can't do anything about it.
This is truly a cruel demonstration.