In general sense, the documentation isn't wrong regarding the use of comma or semicolon as function argument separators.
The separator use in function documentation varies according to the language. In example, the IF function documentation shows comma for English, and semicolon for Spanish and Italian, just to mention a couple of non-English languages.
By the other hand, on a web browser, the function argument separator for some locales could be either a comma or semicolon but it will be changed automatically accordingly to the spreadsheet locale setting. One of this locales is Mexico.
I just tested this, again, using a Chromebook and worked as I described above
Steps to reproduce
Go to http://sheets.google.com/create to create a new spreadsheet . In my case this creates a spreadsheet using the Mexico locale. Additional note, I have enable the Always use functions names in English.
On A1 write
=AND(TRUE;FALSE), the result is FALSE
On A2 write
=AND(TRUE,FALSE), the result is FALSE
Considering the above, the documentation isn't wrong. Maybe we could say that it's not complete or it's not clear enough, as there isn't a note or help article about the use of comma and semicolon on Google Sheets functions.
Changing the local to Germany, the automatically change of the argument separator doesn't occur.