The stable program-kernel interface is not the kernel syscalls, but library API. That's exactly the same as every other non-Linux OS out there including other Unixes and other Free OSs.
Oh, look! They even share the exact same numerical values for the old school system calls. #1 is exit(), #2 is fork(), so on and so forth.
Gosh, on my linux laptop, here in /usr/include/asm/unistd_64.h is pretty much the same numbers, but objectively hidden a little bit more than in the direct Unix descendants. I interpret this as "less documented than in Unixes".
I wonder why that is? Maybe it's because the system call numbers are in fact documented, part of the POSIX API, and descend from Bell Labs Unix source code. Here's V7's list of system call numbers as proof:
Documenting syscalls does not mean a guarantee of stability. I can't recall any other Unixes except Linux which has committed to maintaining syscalls, which means this interface cannot be relied on.