Question: The issuer says a free card can still have hidden onboarding charges. Is that permitted?
Answer: No. RBI directions state that there should not be hidden charges while issuing credit cards free of charge.

Supporting evidence:
title: rbi.org.in/BS_ViewMasDirections.aspx
quote: There shall not be any hidden charges while issuing credit cards free of charge
context: other related charges shall be levied, only on the outstanding amount after the due date, and not on the total amount due. vi. vi Interest shall be levied only on the outstanding amount, adjusted for payments/refunds/reversed transactions. vii. Changes in charges shall be made only with prospective effect giving prior notice of at least one month.

If a cardholder desires to surrender his/her card on account of any change in charges to his/her disadvantage, he/she shall be permitted to do so without levying any extra charge for such closure, subject to payment of all dues by the cardholder. viii. There shall not be any hidden charges while issuing credit cards free of charge.

7. Billing (a) Card-issuers shall ensure that there is no delay in sending/dispatching/emailing bills/statements and the customer has sufficient number of days (at least one fortnight) for making payment before the interest starts getting charged. In order to obviate frequent complaints of delayed billing, the card-issuer may consider providing bills and statements of accounts through internet/mobile banking with the explicit consent of the cardholder. Card-issuers shall put in place a mechanism to ensure that the cardholder is in receipt of the billing statement. (b) Card-issuers shall ensure that wrong bills are not raised and issued to cardholders. In case, a cardholder protests any bill, the card-issuer shall provide explanation and, wherever applicable, documentary evidence shall be provided to the cardholder within a maximum period of 30 days from the date of complaint. (c) vii Card-issuers shall provide the list of payment modes authorised by them for making payment towards the credit card dues, in their websites and billing statements. Further, card-issuers shall advise cardholders to exercise due caution and refrain from making payments through modes other than those authorised by them. (d) No charges shall be levied on transactions disputed as ‘fraud’ by the cardholder until the dispute is resolved. (e) viii Any debit to the credit card account shall be done as per the authentication framework prescribed by the Reserve Bank from time to time, and not through any other mode/instrument. (f) ix Card-issuers do not follow a standard billing cycle for all credit cards issued. In order to provide flexibility in this regard, cardholders shall be provided option to modify the billing cycle of the credit card at least once, as per cardholders' convenience. (g) Any credit amount ari