noun modifier vs adverbial modifier

I am not very sure what the modifier is modifying in the following cases. Can anyone help me out here?

I greeted the boy, playing basketball.
Who is playing basketball? The boy or myself? I think this sentence is grammatically correct but ambiguous. Am I correct? Typically "playing basketball" acts as an adverbial modifier so it means I am playing basketball. But I also found another one from PREP:

Doris Schopper became president of the international council of Médecins sans Frontiéres, known in English as “Doctors Without Borders.”
In this sentence "known xxx" is modifying the noun "MSF" not the preceding independent clause. How can I determine if the participle modifies the preceding noun or entire clause? Thank you in advance.