This statement is true. In The Giver, a member of the community who does not like it there and who does not fit in can apply to leave. Of course, we later find out that a person who does this does not actually get to leave.
We can see clear evidence that your statement is true about 2 pages before the end of Chapter 6 (I only have this book on Kindle and cannot give you a page number). At that point, Jonas and Asher are talking during the lunch break at the ceremonies. Asher mentions that it is possible to apply to leave. He says
It says so in the rules. If you don't fit in, you can apply for Elsewhere and be released.
This clearly proves that you can apply to leave. The problem is that you don’t actually get to leave. We later find out that being “released” means that you get killed. So, the statement is true, but if you apply, it won’t turn out the way you think.