Re: Another example...
This is in no way a circular argument. It's an argument based on historical reliability. I believe Jesus loves me because the historical evidence of his life and words indicates that it's true. Likewise, if I tell you that I honestly love all people simply because they are people that I believe are made in the image of God, you have every rational reason to believe me based on my personal testimony unless and until a defeater of that assumption comes along.
As to the charge of "Jesus loves me this I know, for the Bible tells me so" being a circular argument;
If someone claimed "I know Jesus loves me because the Bible says so, and I know the Bible says so because Jesus loves me", THEN it would be circular.
It is, however, in its current form, simply good history.
Yes, Jesus loves me so, and YES, BECAUSE THE BIBLE TELLS ME SO!