100% wrong. You can't advertise a lower price - for obvious reasons, but you can of course give a lower price to people who call, email or walk in.

Many hotels are idiotic about this and will put a cheaper price on booking, then wonder why booking is taking all their reservations. Unexplainable...

Beyond the TOS nobody reads (not even sellers), this sort of difference might be due to a number of factors. It could well be that they provide rooms discounted to Booking.com because they want to fill a certain amount no matter what, and then do price-anchoring for other rooms on their website. This is more or less like them giving rooms massively discounted to package sellers (Thomas Cook etc).