Thanks for your reply. I checked this out with PayPal directly by phone, and, much to my amazement, they do, indeed, require online banking log-in info in order to confirm that you own the bank account you claim to own. The only reason to link in a hurry to a bank account is to be able to withdraw money immediately from your PayPal account. So I went ahead and went through the PayPal online process, then PayPal showed my account as "verified", and I promptly changed my online banking password to protect myself against the remote chance that this was actually fraud. Turns out to have all been OK and legitimate -- just surprising since it resembles phishing.
I have since used my linked bank account to transfer money from PayPal to that bank account, and it worked quickly and without a hitch.
