there are two sides to all this.
Paypal are bound by UK finance laws, one of which insists that they verify all bank accounts into which fund transfers are to be made. This is to ensure that the account is bona-fide,and that people are who they say they are. The small deposit they make is transfered back, thus confirming that the account is active,and held in the name you provided. They have no choice but to make this verification check if they are to sustain trust in their userbase, and as they have literally millions of accounts the system has to be almost entirely automated in order to work efficiently. the checks are not just a UK thing - all US accounts need to be verified in the same way.
Quite why your bank doesn't want to play ball is beyond me, and I strongly recommend that you take it up with them. You may well say that you don't really care, but it might be the shortest way to get from A to B if you could persuade them to accept the deposit.