Though Wilson was unmarried, dating another woman so soon after his wife's death seemed vaguely scandalous in 1915, especially because, as Starling discreetly put it, Wilson was afraid another woman--a Mrs. Peck, whom the President had known years before--would make trouble if an engagement were announced.
Even though Wilson wasn't married, if he dated someone so soon after becoming a window it might be scandalous. 
Wilson was happily married and has been having an affair with another woman since 1915.