While incorrect data being used for beneficiary fraud happens, census is india is limited in scope by law, and is not used for targeted benefits delivery - there is very little reason to lie here, since the data isn't correlated back with, for eg, your ration card.
NHFS (National Health Family Survey), used here, is a sampled survey (not a census), and has a detailed guide[1] on how they go about accounting for these biases, and ensuring their results remain representative despite sampling. afaik, the results from NHFS have the same limitation as a census - and it is not used for targeting benefit delivery.
You can look at the Questionnaire to get a better idea of how it was administered. It doesn't include any identity numbers (such as ration card or aadhar card), and starts with this:
> My name is _______. I am working with (NAME OF ORGANIZATION). We are conducting a survey about health all over India.
The information on family welfare and health that we collect from households and individuals will help the government to plan health
services. Your household was selected for the survey. I would like to ask you some questions about your household. The questions usually take about 25-35 minutes. All of the answers you give will be confidential and will not be shared with anyone other than members of our survey team. Your participation in the survey is voluntary. If I ask you any question you don't want to answer, just let me know and I will go on to the next question or you can stop the interview at any time.
While incorrect answers are a real thing, surveys can be designed around these problems, with both statistical analysis and better survey design.
[1]: http://rchiips.org/NFHS/NFHS5/pdf/NFHS%20data%20quality%20as...
[2]: http://rchiips.org/NFHS/NFHS5/schedules/NFHS-5Household.pdf