This from the US Department of State info sheet on minors traveling to and from Mexico. It clearly states that a minor not carrying the document described below may not be allowed back into the US. That could be an extremely scary situation for a 16 year old, and an expensive problem for their parents:
Minors: Mexican law requires that any non-Mexican citizen under the age of 18 departing Mexico must carry notarized written permission from any parent or guardian not traveling with the child to or from Mexico. This permission must include the name of the parent, the name of the child, the name of anyone traveling with the child, and the notarized signature(s) of the absent parent(s). The State Department recommends that the permission should include travel dates, destinations, airlines and a brief summary of the circumstances surrounding the travel. The child must be carrying the original letter – not a facsimile or scanned copy – as well as proof of the parent/child relationship (usually a birth certificate or court document) – and an original custody decree, if applicable. Travelers should contact the Mexican Embassy or the nearest Mexican consulate for current information.
Here are the latest state-by-state travel advisories for Mexico. Look up not only the states in which you will be staying, but the states you will be traveling through.
The State Department has a great site and is the ultimate authority on US citizens traveling abroad. Know where the nearest consulate is in the area you travel. This is an excellent example of your tax money working for you.
Have a good time, but stay informed.