Insurance is not about offers or the cheapest deal. Read the fine print and compare different policies both online and offline to arrive at the best solution.
In life insurance, some companies want you to lodge a claim within 15 days only, but LIC is quite liberal. Similarly for car insurance, some companies want theft FIR to be filed in 6hrs. National insurers may be slow but they will not disqualify claims on petty grounds.
Read the inclusions and exclusions for the policies and then shortlist the best one. If a customer has to be enticed with an offer to purchase it, most likely it is inbuilt into the premium. Stay away from freebies.
From personal experience, Bajaj Allianz has been the best. Claimed twice and got 100% reimbursed within 21 days.