I don't think the police took the wrong approach. It was just fueled by what the suspect said. If he would have went in and said "sorry, I just don't feel comfortable talking to you without a lawyer." There would have been no harm. The detective likely would have checked the alibi (ensuring he was at the hotel), relied on the fire investigator's report, and closed the case. But, giving the police more information is only giving them more to explore. Now they may want to look at his financials, did he recently update his insurance, what other debts does he have, are there any weird calls/communications to others, did he purchase anything suspicious, did he conduct any research about arson, etc - and that takes time.