Roughly speaking, in mathematics there are three kinds of statements: Statements which can be proven to be true, statements which can be proven to be false, and statements which can neither be shown to be true nor shown to be false.
With the continuum hypothesis, it has been shown that it cannot be proven to be true, and that it cannot be proven to be false. Unlike what you are stating, there is no reason to believe that it would be true that I would know of, so you should carefully check your source for that information.
There is a famous conjecture called the "Goldbach conjecture", which states that every even number n >= 4 is the sum of two prime numbers. It is considered very very likely that there is no counterexample to this conjecture, but no proof to this conjecture has been found (yet). With this conjecture, we can say that if it is false, then there is a proof that it is false: If the conjecture is false, then there is an even number n >= 4 that is not the sum of two primes. In that case, we could just write down all prime numbers <= n and check that no two of them add up to n, and we would have a proof that n is not the sum of two primes and that therefore the Goldbach conjecture is false.
In other words, if the Goldbach conjecture is undecidable (there is no proof either that it is true nor that it is false), then there cannot be a counterexample to the conjecture, which means it is true.
But this conclusion depends on an argument that is very specific to this particular problem. It works for some other problems, but not for many. And we cannot draw any conclusions from our current inability to prove something. We can only draw conclusions if we can prove that some statement is unprovable.