They are not entitled to make such a requirement. You legally have the right to examine goods purchased by mail order and this obviously involves opening the item.
Advise them that you are rejecting the goods and returning the item for a FULL refund. You will have to pay the return carriage as the item could be classed as not faulty. If faulty eBuyer would have to pay the return carriage.
If you have any problem simply advise them you will take it to the Small Claims Court and that they will also be responsible for your costs.