Except, FALSE. You are not entitled to an attorney when an officer is asking preliminary, pre-arrest questions, like in a traffic stop. So a cop pulls you over and asks you if you have been drinking and you just stay silent? That would be dumb in many situations. I've seen jailhouse lawyers go to jail because they were trying to outsmart cops, too clever by a half.
I know a guy who got arrested for trespassing because he was working out at his old high school gym after hours. Instead of telling the police, "I have implicit permission from Coach XXXX, just call him," instead he just thought he would be clever and say, "I'll just remain silent." Guess what happened then.
I've gotten out of tickets by admitting to a speed I know the cops clocked me at, but who wanted me to admit to a higher speed (I didn't). Had I claimed I was going 65 in a 65, or remained silent, when I damn well knew he had me at 74, I would have been ticketed. Instead, let off with a warning.
And in most states it is not a felony to lie to a cop. It is to lie to a federal agent.
Point being, generic legal advice worded in absolutes is worth roughly what you paid for it.