Lies........liars. Such harsh, ugly words. Branded as a liar......one would hope this is not literally, but suggests that a person was publicly identified as knowingly giving false information in a very serious matter.
False information, knowingly given to.......police......Court......Customs.....Immigration...........statutory declaration. These are serious matters which carry full weight of the law.
Look at the Census as a social / domestic record. I suspect that the enumerator carried a greater degree of accountability than did the informants.
If you are describing your family to be mum, dad and children...why would you volunteer the fact that you are not really married. It is of no consequence to the enumerator or the government.
Inaccurate information about ages are just human vanity....hardly a lie.
Inaccurate information about marital status would be done to avoid censure and embarrassment associated with common law marriages........hardly a lie.
If the Census, or BDM records show information that conflicts with information that you have from other sources, see this to be additional information that you were not expecting to see, and consider what use it might be to your family research.
My examples where incorrect information was really useful -
Alien ancestor, arriving in Australia and enlisting for WW1, needed to be a British subject. He appropriated details of his British-born mother, which details would otherwise have been impossible to locate with accuracy.
Ancestor recording birth of her child, born to unmarried parents, and needing to give marriage date and place, identified details of her own earlier, first marriage. Again, would otherwise be difficult to locate with certainty.
Ancestor dying, second generation of this family in Australia, and death certificate informed by middle aged daughter. In naming parents of the dead woman, daughter was naming her own maternal grand parents. Daughter got one parent right, other name was the daughter's paternal great grandmother's name.
So I know that, during their lifetime, the family of the deceased woman had good knowledge of their ancestors, beyond any means I might have had to know.
You can go through life never giving a false statement, but I doubt that you will have many friends.
Think....unexpected information.......and see what possibilities might follow.
And be measured in describing information as lies, and the informant to be a liar.
Be kind to your ancestors.