The lines I quoted are from Mastering Bitcoin. An I have heard that this book is like Bible for understanding Basis. It says that the private key will be compromised.
Read the quote again:
if the computer you use to sign the transaction is compromised, you risk exposing the private key.
If you import your paper wallet private-key into a compromised PC (for the sake of spending your coins), you risk your private-key (because your PC is compromised).
BUT.... that's just an situation that has nothing to do with the "paper wallet" method itself and should not happen if you do things right:
a) don't get your PC compromised;
b) even better, import your paper wallet to an airgapped device - which is more complicated for newbies - but way safer.