You can't have truly statically linked binaries on glibc systems; they ditched support for that over a decade ago. On the 1% of Linux systems using Musl you can produce statically-linked binaries, but `ldd` will report `not a dynamic executable`.
But it's true that when I tried ldd on a trivial static binary (compiling "int main() { return 0; }" with "gcc -static a.c") I got a different message: "not a dynamic executable". I don't know why you'd get sometimes one message sometimes the other...