As others have explained, the Standard says it's ok, and that the compiler can afford to be lenient about enforcing this because it doesn't affect the caller, but nobody's answered why the compiler should choose to be lenient. It's not particularly lenient in general, and a programmer who's just been looking at the interface then dives into the implementation may have it in the back of their mind that a parameter is const when it's not or vice versa - not a good thing.
This leniency allows implementation changes without modifying headers, which using traditional make tools triggers recompilation of client code. This can be a serious issue in enterprise scale development, where a non-substantive change in a low-level header (e.g. logging) can force rebuilding of virtually all objects between it and the applications... wasting thousands of hours of CPU time and delaying everyone and everything waiting on the builds.
So, it's ugly, but a practical concession.