Protocol dictates that official enquiries in Portugal are channelled through the Portuguese police. However, there are many ways of getting around this as Jenny Murat very publicly achieved in 2007. She was very aware of the very issue you raise.
Jenny Murat was not working outside Portugal or offering monetary reward in exchange for information (afaik). She was not acting for either the police or the victim's family.
What was the attitude of the Portuguese police, via the media, when the Met had seemingly uncovered information which warranted the re-questioning of the 3 burglars?
If a person came forward with information suggesting someone who had already been cleared by the PJ knew what had happened to Madeleine, how would the PJ treat that information? The information may be genuine & justify receipt of reward but if the PJ refuse to follow up the matter then what good would any offer be by the Met?