ALTERNATOR VERSUS DIAGNOSTIC TESTING

[Delia Caribbean]

4.4i 2000 The battery light indicator is red. A mechanic has taken my battery to charge. Says we should then take it to his garage to get diagnostic test - then it will tell him the state of the alternator; whether it can be repaired or if it has to be exchanged.
Someone else said there's no need for the test, as the red battery light on the dashboard is telling me it's to do with the alternator. So they're telling me don't do the test, (the mechanic just wants more money) just ask him to remove the alternator and then get it checked. What do you think?