We don't use public-private keys to encrypt files or documents. We use public-key cryptography for hybrid encryption or digital signatures.
Examples of Hybrid encryption.
RSA as Key Encapsulation Mechanism (KEM)) and AES-GCM as Data Encapsulation Mechanism (DEM). This composition of a KEM and a DEM (data encapsulation mechanism; an authenticated ...
The first source is being imprecise when they say "need". What they mean is that this is one way to accomplish it.
The second source doesn't say what you claim it says.
I suggest studying key exchange protocols and learning how SSL works.