Were these three the last surviving natural born mutants?

Question

In Logan we have the following interactions:

1. While Logan is listening to the radio and a talk-show host says, "It's 2029, why are still talking about mutants?"
2. While Charles and Logan are discussing the past and one of them mentions "they are all gone" or something like that.
3. We later learn that "they" (they meaning some for of government or shadow organization) figured out a way to control mutant births by modifying the world's food source.

Trying to connect the dots does this mean that

Logan, Charles, and Caliban

were the last surviving mutants born naturally? And now,

that those three are dead. Only the genetically modified children remain?

Answer 1

That's what we are meant to believe, Yes

However, I don't recall any hard proof from the film that all mutants had been wiped out. The Doctor towards the end

claims to have done this, in addition to the Westchester incident (a la Xavier)

but we do not know for certain. It's entirely possible that there are mutants left that haven't been killed or died of natural causes yet.

In addition, we know that Transigen has access to multiple mutants' DNA, so there's the possibility of one or two being held prisoner by Doctor Rice.

EDIT: Thanks to this insightful answer from @KutuluMike in the question "What happened to Magneto?" It can also be assumed that some mutants could have fled to other countries, based on the fact that

The Reavers won't follow the children into Canada