risk of attacker decrypting RSA ciphertext without public or private key
When we say "RSA is broken" do we mean that a practical attack is discovered to retrieve the private key from the public, or do we mean that given a ciphertext and no knowledge of either the private or the public key the attacker can decrypt the data?


First off, we always assume the attacker has the public key. Someone saying "RSA is broken" could mean either. The first is a key recovery attack; the second is a message recovery attack. The second (finding $p$ from $c=p^e\bmod{n}$) is what is known as the RSA Problem. It just so happens that currently the fastest way to solve the RSA problem is to recover the private key (think factoring) and then recover the plaintext. It has never been shown that there doesn't exist a better way to find $p$ however (for more on this, see this question).