Fair Use is a legal defence against a claim that you have tortuously infringed someone's copyright. The reason it works is because under Fair Use exceptions there is no tort committed, that is why you get off. It's _not_ the court saying "well you committed a tort against them but it was only a small one" it's the court saying that under the USC there has been no tort committed.
If someone died whilst you were defending yourself, you don't "get off" it's ajudged to be (and considered in the relevant code or statute) acceptable, you didn't murder them. If you murdered them and you win on a legal-defence of "self-defence" then there was a miscarriage of justice.
There are many good guides, http://copyright.columbia.edu/copyright/fair-use/what-is-fai... - note in particular the penultimate para on balance. Even some commercial uses are judged "fair use" just as educational or library uses aren't always allowed. For example Google are allowed to show thousands of DeNiro images on their site under a fair use exception (eg http://en.wikipedia.org/wiki/Perfect_10,_Inc._v._Google_Inc.).
IMO the de minimis use of single, low-pixel size, established cultural images for avatars where there is no actual commercial harm to the image maker and perceivably no commercial gain in the meets with the balanced consideration of the 4 characteristics of fair-use material.
[I've no idea where the page is hosted nor the copyright system in place in the Reunion islands (which may or may not be relevant), do they use French law, are they signatories to the Berne Convention or TRIPs???]
