I have my own personal view on the case that lead me to think there is more to this than abduction.
That being said, if an abduction were true, the McCanns did right turning a stranger away, credentials or not. This woman was not brought in by police. She asserted herself into a situation and asked invasive personal questions. Their child was taken by a stranger and now another stranger is entering their apartment and poking around asking about the child? My guard with be way up around any strangers. How would they know who to trust? I would not speak with her either. I am thinking they only answered her initially thinking it was required. DP was right to warn McCanns.
If this woman wanted to help she could have either offered her services to the police...or merely left a business card with the McCanns saying "call me if you need someone." The way she walked in an flashed credentials I feel was to lend credibility that she was somehow connected to case and police sent her. She did not begin introduction with "I was not asked to be here, just offering to help." She just barged in and IMO let it be assumed she was part of investigation.