I think testing at age 4 is quite inaccurate, but in an asymmetrical way. There are plenty of things that could cause a highly intelligent 4 year old to bomb the test and have their true IQ drastically underestimated, but it's hard to see how IQ could be too drastically overestimated.

As to the "all kids will even out by third grade" axiom, it's propaganda and nonsense. Higher ability kids learn faster (if given the chance) and so achievement gaps increase with age.