If President Clinton were merely being exposed by the media as a sleazy philanderer, then majority US public opinion might have an arguable objection. However, Kenneth Starr's commendably exhaustive pursuit of the Lewinsky investigation, since Clinton had publicly and vehemently denied "sexual relations", is not essentially to do with sex, but has everything to do with the American Constitution and the rule of law.
To uphold those causes, any US president is solemnly required to make an inaugural pledge. Clearly, the rule of law would be undermined if subpoenaed witnesses were to receive signals that to lie under oath is less reprehensible in some cases than in others. Witnesses are sometimes required, for instance, to supply compromising information about themselves in order to corroborate a defendant's alibi.