In addition to what has been said already, I would strongly recommend that you try to picture ATC as a RESOURCE you can use....they are not to be feared.
Presumably, you are comfortable flying radials. I would've asked ATC before reading back the clearance (which implies acceptance of the clearance), "does this mean you'll be vectoring me to the radial, after which I fly to 15 DME, or are you going to send me towards that point after which I'm expected to be able to go direct to the point?"
Even if their initial intention was to send you direct to that point after some initial vectors, I would bet large sums of money that they would've been equally happy to vector you onto the radial and then let you go on your own nav until reaching 15 DME.
The cancellation implies that you are not yet comfortable working with ATC. This is a situation you should try to improve. It's possible to fly VFR without a lot of ATC interaction (I have heard stories of ppl that flat out refuse to out of anything other than non-towered fields, and haven't spoken on the radio since getting their PPL)...but IFR is a different animal.
Don't be afraid to ask 'em questions, you'll be surprised how willing more of them are to help out!