The reason you have to do it on your own is because they rebate company (which is usually not Verizon Wireless) depends on you not submitting it correctly, on time or at all.
Imagine, the rep did 3 hours worth of work to set you up and their shift is 8 hours. How much more time do you expect for the rep to take for you to claim your money? They are supposed to help 2 maybe 3 customers a day?
When there was rebates on the devices, you would get a print out with your name and address already filled in and all you'd have to do is cut off the UPC and put the print out and UPC in an envelope then put it in the mail. The easiest thing to do and people couldn't do it.
You'll submit what you need to submit if you want the rebate or you won't and forfeit the rebate.
Verizon is not in charge of that.