That's true. However, the evidence that people who are trained to recognize lying do any better at it than random people off the street is -- putting things mildly -- not strong.
If they notice you're lying, it will be because you contradicted something they already knew or because you were bad at lying, not because they were trained to recognize it.
Anything more frustrates and angers them.
Incidentally, is this limited to phones? Are they only searching these accounts because they're authed to the phone they make you unlock? Or are they saying "oh, OK, so you're traveling without a phone. Please step over to this kiosk and log into your Facebook account" as well?
Better to have easily restorable backups and just wipe & configure as a "new" device (not connected to cloud services) before entry. Restore from backup when you get home.
This is actually pretty painless these days. Sad that it's necessary.
If you want an Android smartphone that's really cheap go to Wal-Mart. Unlocked Android phones south of $60.
If you can do without a smartphone you can get a dumb or feature phone for ~$10-$30.
There might even be better deals on Aliexpress or somewhere similar if you shop around.
I would call neither _dirt cheap_ for _my_ budget, but that is what I had arrived at as the cheapest possible that is still usable too. "Dirt" cheap, not for me, or probably most Americans, but what can you do.
(FWIW, I think it's no longer possible to get a dumbphone that will work on AT&T for $10-$30, now that AT&T turned off 2G and requires 3G even for voice. More like $60-$80 at the very lowest end that will work on AT&T. Don't know about internationally. :( )
Travel with a safe, clean device, if you travel with a device at all. If it is your employer's device, cooperate and then tell your employer's lawyers what happened.
Stay safe, especially if you're a minority of any kind.
Also "just say that's what you normally do when entering border control" goes against the image you're trying to create.
In any case, if you find yourself in this unfortunate situation (you shouldn't - you should travel with an empty phone when crossing the border, or at least wipe it before crossing then do a restore over icloud later), here's something you can do: Before going in (if you have an iphone), make sure you have a strong alphanumeric passcode. Enable auto-wipe on 10 incorrect passcode attempts. Then, turn the phone off. If CBP then asks to turn your phone on and wants your password, appear eager to comply, but give them an incorrect one, and when that doesn't work, admit that you had just changed it a few days ago to something more secure and that you may have forgotten it, but don't worry, you always just use the thumbprint to unlock the phone anyway and volunteer to open it that way. Always appears helpful. The phone still won't unlock because iphone requires passcode entry after restart. If they ask why you turned the phone off, just say that's what you normally do when entering border control. Unless you're under some kind of serious suspicion of some kind at this time, they're unlikely to detain you for forgetting your phone password, and even if so, it's locked with a strong passcode so there's no much they can do anyway.