The allegation is that, yes he had sex with these women while married to Heidi. If that were not the allegation then the story would be a non story.
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If Ted is innocent, he should go on every news show for the next week and clear the air and this will all be forgotten. Put an end to it once and for all.
Should he take Heidi with him to stand by her man?
Hey it worked for the Clintons, but then they had a complicit press that dropped the scandal like a not potato. Not sure that would suffice as far as the Cruzes are concerned. The press would either drop it for now and bring it up at a later more crucial date if Ted were the nominee, or carry on with it.
Problem is a serious one for Ted, because how does one prove their innocence on an allegation such as this? Simply denying it will convince some while others will remain skeptical.
A more effective course of action is to bring suit against the National Enquirer. That would carry more weight than simply denying it until blue in the face. Because if he is willing to take it to court then the assumption would weigh heavily in his favor of his innocence.
The sister-in-law who supposedly has confirmed the allegation with regards to her sister-in-law, Amanda Carpenter, seems that going to court may not be the best course of action to take either.
So perhaps that is his only course of action, to keep denying the story, albeit an ineffective one.