Here's something I find amazing, professional lawyers not taking their own advice, which is never talk to the police. The 5th amendment, and every Supreme Court ruling ever, is very firm that nobody may be forced to provide testimony that could be used against them. All these "lying the police / obstruction" charges are exactly that, taking someone's testimony and twisting it to be used against them.
If when someone from the justice department "invites" you to an interview, the answer is always "no" or "not without complete and indefinite immunity". The later is never provided outside of very special circumstances so it's pretty much always no.
If a statement would be advantageous, you don't provide it verbally in a closed door interview. Instead it's provided through a lawyer after they've scrubbed it with all the require lawyer words.
Ex
Investigator: Mr Saevel what was the color of your shirt June 8th 2016?
Saevel: Hmm I think it was Blue
Investigator: Well we have another person who said you were wearing red and we want to believe them, so your under arrest for lying.
Yes guys that's how it works. You don't need to actually lie, just the investigating agency has something somewhere that might suggest a different fact of the events in question.
Now here is how that works through a lawyer
Investigator: Mr Saevel what was the color of your shirt June 8th 2016?
Saevel's Lawyer: After discussing the question with Mr Saevel we have provided this public written responce that states
"Saevel in his best recollection believes he was wearing a blue shirt, though the time difference makes it difficult to remember exactly."
Those are the words that prevent a "lying" charge. And because your lawyer wrote it up, had it witnessed and presented it, it's impossible for the investigator to misrepresent or distort it. And never, ever, EVER, sit down in a room with an investigator of any sort, request all questions to be provided you in written format and for you to respond in kind.