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So this explanation would mean that a person could apparently be saved, but not be in actuality, but he wouldn’t find out until some later date when he commits a terrific sin.

To be sure, there are ample New Testament examples of those who appear outwardly to be saved or think themselves saved when they are not, only to later depart. Jesus refers to the Pharisees as "whited sepulchers," the clear meaning being one of outward purity but inward death. Likewise, in 1 John 2 we see that there will be those among the body who appear to be "of us" but later depart and show they were never truly of the body to begin with.

That said...if you are truly in Christ, there is no sin so "terrific" that it can separate you from His love and salvation. It is certainly possible for a believer to fall into sin for a spell, but the devil will never snatch him from His hand and the Spirit will always work to restore that believer to repentance. His salvation in justification is secured because it is purely on the basis of the merit of Christ and none of his own.

One may have subjective assurance of one's salvation, and should be diligent to pursue such assurance, but the objective assurance does not depend on one's subjective confidence in it. Thanks be to God we are His even when we doubt we are so!