OK, that's an actual data point, and I thank you for it, but it's not a very compelling one.

American Samoa, being an unincorporated territory of the U.S., isn't comparable to the 50 states, for many obvious reasons. For starters, the unemployment rate in American Samoa in 2005 (long before the minimum wage increase) was 29.8%, triple the highest rate of any state shown in the graph above.

Furthermore, the population of the entire territory is a shade over 50,000 people, so a single company deciding to lay some people off can have significant effects, regardless of whether those layoffs had anything to do with the minimum wage. If the country were bigger and had more employers, you could make a credible case that it's a trend, but we're really talking about a sample size of two players (Chicken of the Sea and Starkist) that doesn't constitute anything you can extrapolate from.

The fact that the time period in question was smack dab in the middle of the economic crisis also makes it a very poor natural experiment, because the American Samoan economy is so tightly integrated with U.S. demand, which cratered during this time period. In fact, as you can see on page 40 of the GAO report summarizing the employment decline in American Samoa, there was a sharp decline in tuna exports beginning in 2008 that, minimum wage laws or not, created significant problems for the tuna industry in American Samoa.

The "why not $100 or $1000" argumentum ad absurdum really isn't worth engaging. Nobody's asking for $100 or $1000, and the PDF I linked to up-thread provides eleven concrete reasons why we aren't seeing what we might otherwise expect if we followed your simplistic supply and demand line of reasoning. Supply and demand don't vary linearly or absolutely in all conditions.