I'm reminded of a saying from my childhood; 'There's nowt as quare as folk'. Translated it means there's nothing so strange or unpredictable as human beings.
I have a horror of being in the public eye. Others crave it. Celebrities have been accused of being addicted to fame.
Why would fame be desirable to our hypothetical couple? What did it give them? A fan base.
People who believed everything they said. People who wrote to them sending money, cards, toys, love and sympathy. They really appreciated that, it kept them going through the bad times.
It also brought criticism, but they were able to dismiss that. Those who criticised were sad lonely people with nothing better to do, they didn't count.
Fame led to validation by the general public as far as they were concerned. Most people thought they were innocent and supported them. When official interest cooled after they were made arguidos their supporters continued to offer love and support. They were outraged that the pair were suspects. They were outraged that the search was being harmed. No matter what, their fans were there for them.
Popular support needs maintaining. Had they chosen obscurity people would have lost interest and taken up another cause.