Sure, everything is in a database somewhere...
Like paypal, when you add your bank account to your paypal account and pay for something through paypal using your bank account as the method of payment. paypal actually has to call your bank, verify the details and then transact the money. Its not automated, and it cannot be for security and fraud reasons. Thats why there is a 3-4 day period for any amount going through your bank account via paypal.
When you withdraw funds form your bank account or CC to add to paypal...etc. They money is transfered to a Paypal account and a bank. From your bank to paypal's bank. Paypal doesn't actually hold physical money in an office somewhere.
And the online money is really like an account statement that you can access for any interac/debit card. Thats all it is, a balance. Actual money transactions take place via banks and financial institutions.
Because you can imagine what could happen if anyone could just write a script to connect to a bank account...