And "validity," as I noted in an earlier post, basically has to do with whether the theoretical constructs are found to significantly correlate with real-world stuff that goes beyond the specific things that the applicable test asked the subjects about.
And among the things that a personality dimension can correlate with as evidence of its validity is dimensions on other personality typologies — assuming it's not a case where the two typologies' tests are basically asking the same questions. So it could at least theoretically be the case — as LION4!5 suggested — that the correlation between the Big Five and the MBTI offered supporting evidence for the validity of both (although that would be undercut to the extent that the actual content of the test items overlapped).
If you're interested, you can read more about reliability and validity (as applied to the MBTI specifically) here:
MBTI Form M Manual Supplement
And you'll note that the Validity section of the document is where you'll find the studies that correlate the MBTI with several other personality typologies.
As a final point, a personality typology can demonstrate excellent reliability and validity both, but that doesn't make it a "hard science" by most definitions (although you might say it makes it "less soft"). Because the personality/behavioral/etc. things that personality typologies deal with are mostly things where the type stuff is just one among many possible influences, even a highly reliable and valid personality typology can't be used to make specific and falsifiable predictions about, e.g., what a given person is going to do in a given situation.
Like many of the soft sciences (including, e.g., economics), personality typologies can end up making reasonably good predictions when it comes to probabilities — e.g., a prediction that, if I start a personality-related internet forum, it will attract a lot more INs than ESs. But success with respect to those kinds of probabilistic predictions doesn't (by most definitions) shift economics or personality typologies into the "hard science" category.