That's a gross exaggeration. There are certain investigative interrogation tools which do involve strategy which may mislead suspects. Those concepts have been cleared as Constitutional all the way up to SCOTUS. So like it or not, it's a technique which passes muster. However, in general, this is not something LEOs do in the field. And they most certainly are not "trained to lie" in the manner in which you imply, as if it's a common practice.
That would depend on the situation. If the officer is doing an investigation which the person's lies would mislead the investigation, then yes, giving false info would be criminal. But in other situations, it is not a crime. So you've painted with too broad a brush.
That's not bad advice in general. But it may hinder you in other ways. For example, if you are in a situation where you are compelled to ID yourself and fail to do so when legally required, you may be subject to arrest. Whereas if you answer some general questions, you may not have any problems.
As it also should be taught to not jeopardize oneself by running away, pointing a gun at cops, the necessity of following commands, etc. Most of the bad endings to events can be traced to the civilian doing something stupid and/or illegal, then compounding the problems by doubling down and making a dangerous situation even worse.
