Crossword Genius

Argues with presenter falsely promising places (7,8)

Ross

I believe the answer is:

greener pastures

I'm a little stuck... Click here to teach me more about this clue!

'promising places' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'argues with presenter falsely' is the wordplay.
'with' says to put letters next to each other.
'falsely' indicates anagramming the letters.
'argues'+'presenter'='arguespresenter'
'arguespresenter' is an anagram of 'GREENER PASTURES'.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.
Want a hint initially instead of a full solution? Install my app