No, it's really not. Body and flesh are different. For example:
1Co 6:19 What? know ye not that
your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own?
1Co 6:20 For ye are bought with a price:
therefore glorify God in your body, and in your spirit, which are God's.
Rom 7:18 For
I know that nothing good dwells within me, that is, in my flesh. I can will what is right, but I cannot do it.
Joh 6:63 It is the spirit that quickeneth;
the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
Rom 8:9 But
ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
Rom 8:5 For
they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
Rom 8:6 For
to be carnally minded is death; but to be spiritually minded is life and peace.
Rom 8:7 Because
the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
Rom 8:8 So then
they that are in the flesh cannot please God.
Regarding the body changing: I agree with you. The body is sown in corruption (with it's fleshly/natural/carnal nature), however it is raised (without it's fleshly/carnal nature) as a spiritual body:
1Co 15:42 So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption:
1Co 15:43 It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power:
1Co 15:44 It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
Jesus did not die to atone, redeem or reconcile the "flesh" to God. The flesh is still at enmity to God (Rom 8:7), after the death of Christ. "Flesh" is that death in the body that Paul desired to be once and for all rid of (Rom 7:24).
The "flesh" is like cancer in the body. It's death. It's the death to be done away with that God may be the all in all:
1Co 15:26
The last enemy that shall be destroyed is death.
1Co 15:27 For he hath put all things under his feet. But when he saith all things are put under him, it is manifest that he is excepted, which did put all things under him.
1Co 15:28 And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him,
that God may be all in all.