There have been numerous times where I have paid via a card and/or email I use with my PayPal account without using PayPal. It recognizes my email and encourages me to sign in to PayPal to complete the transaction, but I also have the option to complete it without signing in to PayPal. Have done that several times.
On the business side of things, we send out invoices via PayPal quite frequently to people who we know don't have PayPal accounts (they tell us so). We are able to get paid through the PayPal service without them having a PayPal account, but that just may be something unique to the level of service we utilize through PayPal.