I haven't seen the video, I've only read what other people who saw it said but it seems Felipe was greeting the persons who were waiting for them outside the theater (or wherever the Viana Awards took place) and a young woman among the public started talking about why there isn't a debate and a referemdum of monarchy vs republic because there is a minority(really her words
) that it's not being heard. Felipe answers that there was a referendum back in 1978 and she answers that she didn't vote or she wasn't alive or able to vote back then. She asks him to call for a referendum(he obviously doesn't have that power) and then she says he should abdicate. He says he's fulfilling his duty. The president of Navarra was with Felipe and asks her if she doesn't have bigger problems. At the end Felipe shakes her hand and keeps on greeting other people. A friend of hers recorded it and she's been getting publicity for it. It seems it was a polite discussion.
.... and I think, the way they embraced each other, really proves their warm and happy relationship. And why not greeting each other this way, if they were coming from different venues previously? 
