The police can ask anybody they like to come in for questioning any time they like. If one of those persons is a real suspect (= probable cause they were involved in the crime in question) then a failure to let them know they are a suspect could prejudice any later trial.
Kate McCann was made an arguido. Was given fifty questions, of which I believe she answered only one. I dare say her lawyer advised her to keep shtum because what mother with a missing child wouldn't want to tell the police everything they know of the circumstances surrounding it? However, as an arguido (formal suspect), your words can be used against you in court and in any case the burden of proof is on the police and prosecutors, so the reasoning is, 'If they think I did it, let them prove it! It is not in my interest to help them convict me! (Which is what they are after, with their trick questions).'
So when the tabloids report the latest arguido, the German anti-social paedophhile offender (also recidivist burglar and thief) refused to answer the Portuguese police's questions as an arguido as to where he was on the night the little girl went missing, it is not really so strange he refuses to answer.
The papers report that the McCanns 'welcome' this development. I wonder if this is because they themselves can no longer come under suspicion. That has to be a relief, I guess.