It is true that any strong symmetric encryption generates data that it is indistinguishable from random for any (efficiently computable) statistical test, but t

It is true that any strong symmetric encryption generates data that it is indistinguishable from random for any (efficiently computable) statistical test, but these tests are extremely weak and don't prove anything. All but the last two only look at distribution of the bytes, meaning that the string "\0\1\2...\255" repeated many times would give the same values, but it doesn't look random at all. The Monte Carlo computation of Pi also ignores the order (sums are commutative). The serial correlation coefficient only looks at the correlation between the sequence and itself shifted by one, ignoring higher-distance correlations, so it almost as easy to produce very regular sequences that have give very small coefficients.