I confirmed that what the OP described is something legit on the PayPal website. Login to PayPal and select Wallet on the top menu and "Link a Bank" (https://www.paypal.com/myaccount/money/banks/new)
Select a bank, then it will ask for a user/password login at the bank. PayPal’s description is:
PayPal is using Yodlee, a third party financial service (https://www.yodlee.com/company). Personally, I feel more comfortable using the traditional routing/account numbers.
Select a bank, then it will ask for a user/password login at the bank. PayPal’s description is:
We use Yodlee to confirm your bank details and to check your balance and transactions as needed, which can help your PayPal payments go through. For more information, see our Privacy Statement. You can turn off our use of Yodlee by removing permissions for this bank in your Profile.There is an alternate option if you look at the bottom:
Link your bank another way (Takes 2-3 business days.)In this case you would enter routing and account number.
PayPal is using Yodlee, a third party financial service (https://www.yodlee.com/company). Personally, I feel more comfortable using the traditional routing/account numbers.