Its been too long for me to vouch for but I do remember that all the tabloids were VERY interested in solving this case. And the Enquirer actually gained some credibility when it verified that OJ Simpson actually DID own a pair of Bruno Magli shoes (remember? he claimed he wouldnt "wear those ugly ass shoes" and then the Enquirer had that photo to prove him wrong). Ever since the Enquirer lost that lawsuit to Carol Burnett, they've tried to clean up their reporting and have been careful to attribute their sources and to be more accurate in their wording
Possibly (again, its too long for me to say for sure) the Ramseys felt that the Enquirer was the most persistent in their coverage and decided to give an interview? I dont know....