You are confusing the court and the cops. Everything you write is true about court. But it's not true regarding cops.
Cops do not need proof to arrest someone, they simply need to be suspicious. You want them to not be suspicious of you, and the easiest way is not to act guilty.
Asking for a lawyer does not fall under probable cause, which is what they need to arrest you. "He looks guilty" is not probable cause. And if they already have cause, you really want to have an attorney present. I don't understand why this isn't completely obvious.
I'd suggest taking the time to speak to someone in law enforcement about how difficult it actually is to perform arrests. I think you would be surprised.
The police were already suspicious of the guy as he received a letter in the mail to come down to the police station. Why are you so insistent on talking to police without a lawyer? People watch too much TV to think that "not acting guilty" will get you bonus points in the real world. Also, police job performance is not measured by letting innocent people go. It's measured by arrests and convictions.
Cops do not need proof to arrest someone, they simply need to be suspicious. You want them to not be suspicious of you, and the easiest way is not to act guilty.