The implication is that while different people and organizations can be pretty close to the same figure for the size of the application, the effort estimate can vary substantially across different organizations.
Sizing done using Function Points is verifiable since it uses a generally accepted method. In contrast, the other popular method of computing effort- the Work Breakdown Structure (WBS) is almost entirely based on implicit productivity of an organization or team. The productivity factor that uses the FP count also makes it easier to compare the productivity across teams and organizations.
Another aspect of Function Points is that it is based on statistical techniques, and hence small variations in the computation tend to cancel out each other. Despite this, it is very reasonable to see a variation of 15% or so in the calculations done by different people or teams even when using identical inputs. For larger projects, I prefer to have the estimation done independently by two teams and then have it cross checked with an estimation done using WBS. Then use a mean of the three.