If Christians "have" (whatever that means) no fallen nature, then what is it that plagues them still? Is that not the "Old Man", of Ephesians 4:22 and other places? It is not just 'this tent'.
Let's go by what the Bible says, shall we? I hope that we agree on Sola Scriptura.
Our body is a "tent", but that analogy is not particularly helpful, in this context, since it does not address the attributes and effects of that tent.
Rom. 7:22-25 (EMTV)
22 For I delight in the law of God in my inner being.
23 But I see a different law in my members, waging war against the law of my mind, and capturing me by the law of sin which is in my members.
24 O wretched man that I am! Who shall deliver me from this body of death?
25 I thank God through Jesus Christ our Lord! So then, I myself with the mind serve the law of God, but with the flesh the law of sin.
Here, we see the continuing contrast between a Christian's inner being and the flesh (outer being) with its members (parts). It is referred as "this body of death"; in other words, it is, from a spiritual point of view, the mortal enemy of a Christian, from which he needs to be delivered. The means of that deliverance (as with all our deliverances) is through the Lord Jesus Christ.
The renewed mind serves God's law, but the flesh (body) serves the law of sin.
Rom. 8:1-4
1 There is therefore now no condemnation to those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit.
2 For the law of the Spirit of life in Christ Jesus has set me free from the law of sin and of death.
3 For what was impossible for the law to do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, and concerning sin, He condemned sin in the flesh,
4 so that the righteous requirement of the law might be fulfilled in us who do not walk according to the flesh but according to the Spirit.
Those who are in Christ do not walk (i.e. live habitually) according to the flesh (body - outward being) but according to the Spirit (who dwells within us, in fellowship with our born again human spirit); and there is no condemnation to us.
The law was weak (even in the life of a Christian) because of our flesh (body - outer being); but, God has solved the problem, by sending his Son, in the likeness of sinful flesh (he had a body that looked like ours, even though his was sinless) and condemned sin in the body, when Christ died in his sinless body, on the cross.
The righteous requirement of the law (singular - i.e. love) is fulfilled in us who do not habitually live according to the sinful body, with its various sinful desires, but according to the Holy Spirit.
Rom. 8:9-14
9 But you are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. But if anyone does not have the Spirit of Christ, he is not His.
10 But if Christ is in you, the body indeed is dead because of sin, but the Spirit is alive because of righteousness.
11 But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you.
12 Therefore, brothers, we are debtors—not to the flesh, to live according to the flesh.
13 For if you live according to the flesh you shall die; but if by the Spirit you put to death the practices of the body, you will live.
14 For as many as are led by the Spirit of God, these are sons of God.
We are not "in the flesh" (i.e. not controlled by the sinful impulses of our body - outer being), but in the Spirit (i.e. led by the Holy Spirit), if He dwells in us.
If Christ is in us, then the body (flesh - outer being) is dead because of sin, but the spirit (I believe that this should not be capitalised here but refers to our born again human spirit - inner being) is alive, because of the righteousness of Christ.
Verse 13 is especially appropriate here: if we live according to the flesh (body), we will die; but, if we put to death the practices of the body (flesh) we will live. We see here that the terms "flesh" and "body" are used interchangeably, in a form of contrasting parallelism.
As many as are habitually led by the Spirit of God, these are the sons of God (as contrasted with those who are habitually led by the sinful impulses of their flesh/body).
But your question is asked from a temporal point of view. The "fallen nature" goes to Christ, and it happened at the cross, and whatever there may be relevant in that atonement. Sin is not just sins, but sinfulness. I hope you don't pretend not to sin or be rebellious anymore —is it the corrupt material of the flesh, or the corrupt nature, by which you are enticed and rebel?
Don't start any nonsense insinuations that my position might mean that I "...pretend not to sin or be rebellious...". I won't put up with that kind of underhanded tactic.