Some of the confusion here seems to come from meaning of continue runway heading and fly straight ahead. runway heading is a vector, you fly the 'heading' of the runway centreline just as you do any other heading issued by ATC whilst straight ahead means that you
track the extended centreline (easier if there's a localiser I guess!). In the former case ATC will worry about wind in the latter the pilot has to.
If we go back to the original question
On departure the SID calls for straight ahead to 3miles then a left turn to hdg 330. After taking off i engaged the autopilot and the aircraft started to turn, much to my bemusement. As I disengaged the autopilot to hand fly the correct heading, ATC calls me and says "maintain runway heading" in a slightly scolding tone. I took this as a rebuke for not sticking to the assigned runway heading on the SID, and continued to fly the departure with my tail between my legs. At 3 miles I turned left hdg 330 as per the SID, and on reaching the heading ATC says "say your hdg", to which I replied "330". ATC says " I told you to maintain runway heading " and so I then turned back onto runway heading feeling like a complete idiot. Only later did i realise the HDG mode was following the bug on the copilots side.
The SIDs that I have worked with have almost always described tracks to be followed (the exception being those which included a heading for a short distance after departure before turning to intercept a track).
If capster's recollection of events is correct, ATC's instruction to continue runway heading sounds like it was a revision to the previous clearance (the SID). The business about whether ATC can or should do this below MVA is a different matter entirely......