I understand that several historic buildings in Scotland - for example Traquair House, Blair Castle, Greyfriars Kirk - have walls of pebble-dash (which is called 'harling' in Scotland) painted cream or pale yellow so as to resemble the original lime-based covering. In the case of the Kirk, the overpainting was a condition of obtaining a Lottery grant for the other elements of the restoration.
Harling is a popular house finish in Scotland, and the famous multicoloured seafront row of houses in Tobermory (Google for it!) shows how frequently and enthusiastically it gets overpainted. I know of scores of other examples both locally and nationally. You would therefore have good reason to doubt whoever was advising you not to do it.