Two totally different harmonies can support the same melodic line. Can someone still be accused of musical plagiarism even if the melody has been reharmonized? Wouldn't that be to assume that the underlying harmony doesn't have a drastic effect on the feeling of a melody?
An example of a work being successfully pursued for royalties based on a melodic fragment played over different harmony is "Kookaburra" as quoted by "Down Under".
In theory, someone could be accused of musical plagiarism on almost any musical basis. Cases have been won recently based on pieces having similar instrumentation and 'feel' - and although I can't find a link, I recall reading about a case being made on the basis of two songs featuring a similar sound, even though the sound was a preset from a popular synth.