Yes, if the desire of the persons heart is to remain in Christ, you are correct. Yet, there are those who do turn away that were once in Christ.
Hebrews 6:4-6
For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an open shame.
These will loose their salvation. There is no way that anyone can read these verses and claim that they were never a true Christian.
In relation to the last sentence of the quote above, what I find intriguing and frustrating about the quoting of Hebrews 6:4-6 is that people never seem to quote the following lines:
Hebrews 6:9 Even though we speak like this, dear friends, we are confident of better things in your case