I think it is highly likely that many words clash that way. Worse, I expect many clashes between words that fit the crossword description. Consider, for example, a description of 'animal'. Now, look up a few animal:
So, there is some variation, but it isn't hard to find immediate collisions, especially for related words. That makes sense; a dictionary should not attempt to vary the way it describes similar words.
http://www.merriam-webster.com/dictionary/elephant: any of a family (Elephantidae, the elephant family) of...
http://www.merriam-webster.com/dictionary/rhinoceros: any of a family (Rhinocerotidae) of...
http://www.merriam-webster.com/dictionary/crocodile: any of several large...
http://www.merriam-webster.com/dictionary/buffalo: any of several wild bovids...
So, there is some variation, but it isn't hard to find immediate collisions, especially for related words. That makes sense; a dictionary should not attempt to vary the way it describes similar words.