It absolutely depends on their policy. Generally those that aim for a certain market of non-tech savvy users do offer a plan with little controls and then charge for mundane things like MX records. I've even had one ask for money to activate the 'firewall'!
This is not common practice for more reputable places and most - even very cheap solutions - will generally have an interface for customers to change custom MX records and provide free-of-charge support to change configuration not available in the self-serve interface.
The bottom line is that you must read and ask questions, if uncertain, exactly what you are getting for the price advertised. There are all sorts of plans with arbitrary limits to distinguish each other even if there is no different in H/W and S/W required on the hosting provider's part!