Yes, Centrelink do call to get information.
The safest way would be to ask for their contact details, and for your to call them back via their main number (number advertised on their website).
Years ago (8 or 10 years ago), when they first brought out depositing childcare rebate directly into parents' bank account, I received a call from Centrelink.
I confirmed what they told me over the phone, but when they start asking me to provide more personal information - I told them that I have no way of knowing whether it is a scam or not, so can I have their details instead and I will call them back.
Yes, I won that round, but I have been receiving cheques in the mail for childcare rebate since then - need to make a special trip to the bank every 3 months to deposit them :-(