Here is the scenario,
I have a public domain "domain.com". I need to point this c125.example.com.
Note: I am not the owner for example.com.
Will I be able to create an alias domain.com without any prefix which point to c125.example.com for DNS resolution.
Note: With prefix, it works.
You won't be able to do it with a CNAME because that breaks the "CNAME has other data" rule.
But you could try using a DNAME. Create domain.com and add a DNAME record with an empty host name, point it at c125.example.com. See if that works.
PCN (UK) Ltd
All opinions expressed are my own and not representative of PCN Inc./PCN (UK) Ltd. E&OE