Well, if you look at the raw score to scaled score conversion, you can see that the last half-dozen or so raw score points change the scaled score more rapidly than the middle twenty or so points do, which is a simple visual for the decrease in spread that happens at the extremes. A 560 is much closer to the middle of the curve on the SATs than it is on the PSATs, which typically means more fine-grained distinctions between one level of test performance and the next. This is similar to the discussion that frequently comes up around here about moving from the MAP primary (K-2) level to the MAP 2-5 level test in elementary school. Once you enter the upper 90s %iles on a test, a careless error or chance correct response can skew the apparent performance significantly. A test is most accurate when performance falls near the middle of its range.
But yes, for some students, the PSAT will give sufficient information during another round of testing to put off transitioning to the SATs a little longer. It depends on your child's needs, and what function the testing has for your family.
