Perhaps as a general definition, but singing is an art of using the human voice to create music. There are occassions when being completely off key and off time, and various sounds that may be deemed unpleasant, can be used in music to create a statement, granted that it can't be heard in contemporary music. (i.e. Christina Aguilera felt she was "pitchy" on her first and only vocal take on "Beautiful;" Linda Perry said that was perfect, as Aguilera's vocal imperfection adds to the message and theme of the song.) And yes, staying in pitch can be one of the main elements of the universally acknowledged criteria of singing, but my argument is that that aspect alone should not make one a singer, as there are other aspects to consider. Otherwise, we might as well save singers the trouble and have computers, robots, and vocoders do the work for them.
And the comparison to sports is not really fair, considering sports is full of technicalities whereas in the arts, anything goes. Granted, more mainstream music built up certain criteria singers have to meet in order to create marketable work, but as an art, singing has no rules. Even spoken word can be defined as singing by some on occassion. But as an art, it still has to have intention, message, emotion, or a combination of some. At least to me, that's what makes one an artist. A more fair comparison would be pitch is to singing what a paintbrush is to a painter. Yes, it's a more common tool used in painting, but the painter could experiment with painting with paper, his fingers, etc. and still be a painter.
Mary J. Blige sings with emotion, intent, and message, so regardless of whether or not she can stay on pitch, the girl can sing.