Only USNA admissions would know what (if any) impact the change to the SAT format will have on their admissions process. Personally, I have NO idea what magic the person in the above article provids for the $1,000/hr he claims to charge. Probably, he is more concerned about how this might impact his apparently lucrative tutoring business.
I guess if your parents have that kind of money, they can certainly spend exorbitant amounts on 'tutoring' in the hopes of increasing SAT/ACT scores. If a student struggles with math (as an example) all during h.s., no amount of SAT/ACT 'coaching' will change that.
As it relates to service academies, the best general advice is to take BOTH tests since some tend to do better on one than the other. SA mostly use them as a standardized way to compare h.s. students having varying academic backgrounds. Whether or not such tests are a predictor of future success will always be the subject of endless debate. Also good to remember that even if the SAT changes for 2016, you are still taking the test with every other h.s. student.