I really don't think that this was specifically developed in response to law school admissions. Ding is a VERY common colloquialism which can be used to describe any sort of detrimental response to your performance by a higher up.
For example, if you were coming up for your yearly salary review and you had some bad mark in your file, it would be called a ding. Also in something like a quality control evaluation, a defect would be a ding on the report.
Very common, at least in the work world...I would venture that the term crept into law school admissions, not t'other way 'round.