They are pants on fire lying to you. There are two plugs on the diff. a lower magnetic plug and an upper fill plug.
The only way to know that there are shavings in it is to pull the lower plug. and if you pull the lower plug all the oil come out. so he would have effectively changed the oil for her.
Now, the good part. he is right, you do need to change your gear oil. How do I know? Because no one ever does it and it should be done every 30000 miles or so.
And if you can change your own oil, you can do this. its simple.
Oil drain pan under read diff.
Remove upper plug, set aside.
Remove lower plug and drain out the gear oil.
Clean the lower plug, inspect for shavings.
Replace lower plug
Fill top opening with new gear oil (I use Mobil 1 synthetic).
Diff is full when the oil get to the lip of the fill opening.
Replace top plug.
You are done.