To be more precise, I think this does not mean we are saved from the ACT or even the TEMPTATION of committing sins. Rather, we are saved from the CONSEQUENCES of committing sins. Therefore, we have to ask what are those consequences: leading an unholy, unrighteous life and thus being separated from G-d. Next question: is this separation only in our earthly life or does it continue in the hereafter in the form of hell? Also, can this separation be repaired, and, if so, by what means, to what extent, and when? These, I believe, are some of the issues that must be considered when talking about sin and salvation.
One other point. The Bible does not tell us everything explicitly. There must therefore also be a means of filling in the missing parts of the ideas that the Bible discusses.