Even I faced the same problem a few months back. What the bransh staff says is correct - ICICI has infact stopped regular savings account.
You can open a savings account with 1L initial funding - that is the lowest regular savings account that you can open with ICICI.
(some branches agree for 50k). This account variant is called Privilege.
Some branches will push for 3-in-1 account. - in this case, they will deduct 999 + GST after a few days of opening the acocunt towards demat charges.
third way - if you are salaried, open a salary account and don't make it your salary account (means, don't give this account details to your employer). It will be 0 balance account for 3-6 months and after that, they will convert it to regular savings account with 10k MAB requirement. (again, depends on your luck, for many people, this conversion never happened, and ICICI doesn't care much, but maybe going forward, it will be stricter)
Apart from this, you cannot open a regular savings account in ICICI bank.
@OptiCard can throw more light here.