There are usually at least two sides to every story. In this case Travolta's law talkin' guy Marty Singer is there to present the B side. According to Singer these allegations are “false and outrageous”. Singer also goes on to point out that these stories go back 15 years, yet Randolph has only just recently brought them to light. Singer then goes on to point out that the idea that Travolta “engaged in multiple adulterous sexual encounters in different public locations in Los Angeles (where he does not live), and that each time, the (nonexistent) events were coincidentally witnessed by [Randolph], is absolutely ridiculous.” Singer then goes on top point out that Randolph - by his own admission - suffers from permanent brain damage. According to Singer this adds up to “blatant defamatory lies” from a “patently unreliable source.”
Now when your good name is besmirched like that the usual recourse is to the law. So Travolta and Singer are suing. They claim that Gawker is “significantly compounding the damages” incurred by Travolta. With that in mind Singer is demanding - on Mr Travolta's behalf, that the Gawker immediately and permanently remove said article from their site & and publish an “unequivocal and prominent retraction of the false and defamatory statements.”
If you're gonna take aim at big game like that then make sure you've got a unimpeachable source, or at least some one without brain damage. Without the wonder, it's just trash.