A Tricky Phrase 'be down to'

A Tricky Phrase 'be down to'

I've got the passage below from Invisible Monsters by Chuck Palahniuk.

My inventory of people who can save me is down to just me. Not my best friend. Or my old boyfriend. Not the doctors or the nuns. Maybe the police, but not yet.

I want to ask a question regarding the underlined sentence.

Dictionary says 'be down to' has two meanings,

One is "It's down to me to find a suitable person for the job,"
meaning "to be someone's responsibility or decision".

The other is "I'm down to my last few dollars,"
meaning "to be left with only (the specified amount)."

On the surface, the phrase in the sentence in question seems to mean the former.
But in deeper contextual sense, it really seems to mean the latter, that is...
The lead character reflected on who can save him in the desperate situation but came to the conclusion that nobody can save him but himself.

Do you agree with my line of thought?

Regards.