this sounds odd but right at the same time!
I'm sure they have tightened up on this but i presume they are seeing it from the point of view of anyone could ring up and cancel any ticket purchase maliciously HOWEVER
you are spot on that they would refund the card it was purchased with which was yours.
I personally would call back again and try your arm - suspect they will process it but i can see why there may be a policy like that as i say
That said can you imagine the number of calls they would create for themselves! Also a bit of a farce if they would have refunded had you just given the DOB - doesnt rule out the malicious angle i presumed would be their driver for the policy
All in all i reckon i've been sod all help there