Good investigators withhold details about a crime from the public mostly to filter out false confessions. This speaks to the fact that false confessions are common enough to make filtering techniques common practice.
That's not the only goal. This also reduces the effectiveness of copycat crimes, and differentiates any would-be copycats from the original. Also, it enhances the ability of authorities to receive and authenticate tips from the general public. In fact, in a high-profile case, it's common practice to deliberately plant misinformation in the form of slight immaterial errors, for many of the same purposes.
I think you're talking about Lucia de B. The first sentence of the article :
When a Dutch nurse named Lucia de Berk...
In fact, she never confessed. As per her Wikipedia page:
Important evidence at the appeal was to be the statement of a detainee in the Pieter Baan Center, a criminal psychological observation unit, where de Berk had said during outdoor exercise, "I released these 13 people from their suffering". However, during the appeal, the man withdrew his statement and stated that he had made it up.