Sorry but lawyering up is the smart thing to do when talking to the police. That’s not proof of anything.
“Some Puerto Rican guy.”
It's not that they just lawyered up, it's how they refused to cooperate with the police when they as a family would have been the best source of information as to why this murder happened, no matter what theory one ascribe to. It sometimes took months or even years before the police were informed of stuff they should have gotten in the first few days .
Lawyering up is reasonable, but it's definitely not reasonable to behave like the Ramseys did and how they were given information about the investigation that they had no right to, they went so far that another father whose daughter had been murdered was making a plea for them to cooperate with the cops for the sake of their dead daughter.
Because it sure seems like they weren't too keen on finding out who did it, there are a number of newspapers stories from that time that asks why the Ramseys were hiding behind their wealth and also blaming their own legal representation for not letting them talk to the police, when they were the ones who decided what they wanted to or not.
It's one of the things I find most disgusting about this case, Ramseys going on tv or to newspapers/tabloids to lament about how they for sure wanted to have a working relationship with the police, but when off air they put such ridiculous restrictions on any meeting that even the FBI told the police that "you don't give in to those demands", and the sentiment at the time in the locality was that if they were innocent why behave like this and putting even more suspicion on themselves instead of cooperate.
As everyone else I have no clue who really killed Jonbenét, but the Ramseys behaviour haven't ever stuck me as parents who really wanted to know, because they already knew.