You are correct that no born-again believer can be possessed by a demon. Being possessed means that a demon controls a person, and the person has little control over himself.
A born-again believer is someone who belongs to God. God the Holy Spirit is in that person and therefore that person cannot be possessed by any demons.
The Bible tells us: “You are from God, little children, and have overcome them; because greater is He who is in you than he who is in the world.” (1 John 4:4).
So if we trust God, we have overcome them. We do not need deliverance ministries to deliver us. But God delivers us from all evil (Matthew 6:13).
It is my opinion that many deliverance ministries are not good. In fact, many deliverance ministries do things that dishonor the Holy Spirit.
Years ago, I attended a deliverance ministry event.
I saw people fall to the floor unconscious, because a “pastor” would exercise a spiritual power over the person and cause that person to fall to the floor. The “pastor” could not make me fall over supernaturally. But he took my head in his hands and pulled me toward him. I was losing my balance because he held my head and only my toes touched the floor. Then he pushed me backward onto the floor. So that was how everyone ended up on the floor. They either got pushed over physically or pushed over spiritually. Either way, it was not good.
We know that there are many false teachers and false prophets already in the world (1 John 4:1). “For false Christs and false prophets will arise and will show great signs and wonders, so as to mislead, if possible, even the elect.” (Matthew 24:24)
These false teachers can also perform signs and wonders to mislead Christians.
The teachers of these deliverance ministries, knowingly or unknowingly, exercise a kind of spiritual power (not from God) to influence Christians in such a way so that they roll on the floor, bark like dogs, laugh or dance uncontrollably, bend over double, and do other similar things. Note that these acts are very dishonoring to the person and to God. Such things are actually making fun of God, especially the Holy Spirit.
The Holy Spirit is gentle and kind. He would never force a person to the floor to roll around and bark. But people who don’t know God, pretend to be teachers, and mislead Christians. As children of the Most High, we are to possess our own vessel in sanctification and honor (1 Thessalonians 4:4).
“Likewise urge the young men to be sensible; in all things show yourself to be an example of good deeds, with purity in doctrine, dignified, sound in speech which is beyond reproach, so that the opponent will be put to shame, having nothing bad to say about us.” (Titus 2:6-8)
Because we are children of God, we ought to conduct ourselves with dignity. Such acts by these deliverance ministries dishonors God and people, because such acts degrade people (e.g. making people bark like dogs, roll on the floor like crazy, etc.). Christians would come under the influence of these powers, because they submit to them and believe in them. But they are being misled.
Jesus said, "Not everyone who says to Me, ‘Lord, Lord,’ will enter the kingdom of heaven, but he who does the will of My Father who is in heaven will enter. Many will say to Me on that day, ‘Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?’ And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness.’" (Matthew 7:21-23)
Look at the lives of the ministers of these deliverance ministries. I know of several leaders whose lives are not marked by being a good example to people. In fact, one of them publicly stated that it is ok if their spiritual lives are messed up as long as they exercise and practice these spiritual gifts. But this is contrary to what the Bible teaches. We need to obey God as Christians as Jesus tells us. And if they are not doing that, they are practicing lawlessness and not listening to God. They are performing signs and wonders as false teachers.
So it is best if Christians refrain from going to deliverance ministries (many of which are not good), because God delivers us from all evil. The Bible instructs us on what to do if anyone is sick or has sinful addictions: “Is anyone among you sick? Then he must call for the elders of the church and they are to pray over him, anointing him with oil in the name of the Lord; and the prayer offered in faith will restore the one who is sick, and the Lord will raise him up, and if he has committed sins, they will be forgiven him. Therefore, confess your sins to one another, and pray for one another so that you may be healed.” (James 5:14-16)
If anyone is sick or have sinful addictions, that person should ask others in his own church to pray for him. As we repent of our sins and pray for one another in faith, God will help us in all things.