Question about confusing results

[Guest]

I have a couple of good friends from California. They were diagnosed as HIV+ back in the late '90s - multiple tests, confirmatory tests, the whole 9 yards.

A few months later they moved to France (one of them is dual national). They were in their late 20s at that time. The two arrived in France tested again for HIV so that they can enroll in the national health programme. Oddly enough, both had their tests come back as negative. They tested about a dozen times, all negative. Happy campers, they settled in their life pretty well. 

Late last year, after almost 30 years, they moved back to California and they found out that their old records were still showing them positive. So, without second thoughts they tested again. Surprise, surprise they tested positive again. They were then told that the testing standards in California are different than the ones in France. 

So, my question is how can you test positive in US but negative in France? I've heard of false positives or negatives, but this is a first... and how come the standards of testing and results are different?