I'll try to explain it...
If your employer pays your Brobizz and doesn't deduct tax for this from your pay-check, then your employer is correct when he says that you can't get your commuters deduction...
If he on the other hand pays it, and then deducts the tax from your pay-check then you are allowed to get commuters deduction...
So what he told you is correct, with the exception that this is not a new rule...
If you decide to get taxed, and get your commuters deduction you will be allowed to declare a deduction of 50 DKR for each time you cross the bridge for a work related cause... For example a normal day where you drive to DK in the morning, and back to SE in the evening will give you a deduction of 100 DKR.
Note as well that if you are not getting compensated by your company for driving to and from work, you will also be allowed to get mileage deduction...
Hope this makes sense :)