The court made the observation while declining to pass any interim order on a plea of the West Bengal government that the citizens should not be excluded and denied social benefits for want of Aadhaar or due to its non-authentication.
"These kinds of problems may not be a ground for holding a statute unconstitutional," a five-judge Constitution bench, headed by Chief Justice Dipak Misra, said.
The bench, also comprising also justices A K Sikri, A M Khanwilkar, D Y Chandrachud and Ashok Bhushan, asked senior advocate Kapil Sibal to continue advancing his arguments on the aspect of exclusion of citizens and made it clear that it would not pass any interim order.
Mr Sibal, referring to a news report, said that some persons have been denied old-age pension on account of Aadhaar and sought an interim order so that nobody is excluded.
Attorney General K K Vengopal and Additional Solicitor General (ASG) Tushar Mehra, appearing for the Centre and the UIDAI respectively, opposed the submission of Sibal that people are being denied the benefits for want of Aadhaar or its non-authentication.
"If biometrics and iris scans fail, you are entitled to produce any alternative ID," Mr Venugopal said, adding that there was no question of any exclusion.
The attorney general said that a person, who does not have Aadhaar, can seek benefits on the ground of that he or she has enrolled for it.
ASG Mehra referred to a note of the cabinet secretary to highlight that steps have been taken to handle exceptional situations and such arrangements have been made in all blocks and talukas to have alternatives available for citizens.
"This actually indicates a country-wide problem. And the question is whether until mechanisms are placed, nobody should be excluded," the bench said.
However, the court also observed that the government said that 1.2 billion people have been enrolled and it meant that only ten crores are left and "if there are so many problems, then how so many people been enrolled".
There was a difference between getting enrolled and having to authenticate each time, Mr Sibal said.
The bench said the exclusion may be because of the infrastructure problems and the government may upgrade the system.
Senior advocate Rakesh Dwivedi, appearing for a state government supporting the Aadhaar scheme, referred to the provisions of the 2016 Aadhaar Act and said that a person was needed to show only the Aadhaar number for availing benefits if authentication failed.
Mr Sibal, during the one-and-a-half hour-long hearing, referred to the United Kingdom's national biometric identity project which was scrapped in 2010.
It was claimed that the bill would lead to less illegal migration and enhance ability to fight terrorism, he said, adding similar arguments are being made here as well.
The UK Bill was scrapped on grounds including "the government is a servant of the people, not the master," Mr Sibal said.
"My entitlements should depend on my status, not on my identity. I might be a pensioner with a pension card issued by the government, but it can still deny the benefit," he said.
On the issue of Aadhaar being used as an identity card, Mr Sibal said, "Passport, PAN card, driving licence and water, telephone and electricity bills are acceptable by authorities as identity cards. Then what is the intent behind compelling the citizens to go for Aadhaar".
The bench then asked Mr Sibal whether Aadhaar can "harmoniously" co-exist as an ID card with other IDs.
"If it is voluntary, then there was problem," the senior lawyer responded, adding that there should be right to choice.
The advancing of arguments would resume on February 13.
Earlier, the top court had questioned the West Bengal government for its stand against the Aadhaar scheme, saying what was wrong in having 'one-nation, one-identity' for all Indians through the measure.
It is hearing pleas challenging the constitutional validity of the Aadhaar scheme and the enabling 2016 law.
The top court had on December 15 last year extended till March 31 the deadline for mandatory linking of Aadhaar with various services and welfare schemes of all ministries and departments of the Centre, states and Union territories.
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