Dealer Guarantees Easy Claims - Then why not choose the cheapest (reasonable) policy?

My car’s own damage (OD) insurance is up for renewal. When I bought the car, I went with TATA AIG through the dealer. Now, I’m considering switching to HDFC Ergo or ICICI Lombard, since their premiums are much lower than TATA AIG for the same coverage and add-ons.

The dealer is offering me policies from four different insurance companies, all with identical benefits, add-ons, and coverage. When I asked why I should purchase from them instead of directly from the insurer, they promised that if I buy through them, they’ll handle the entire claims process and ensure a hassle-free experience at their service center.

Now, this is what’s bugging me:

If the dealer is guaranteeing support with claims and all the policies have the same features, is there any reason I should pay for a policy with a much higher premium? Is there a hidden catch I’m missing, or is it safe to just go with the cheapest option among the dealer’s offerings? I understand the claim settlement ratio could be a factor here, but I’m wondering if the dealer’s promise is worth considering. In that case, it seems logical to go with the one with the lowest premium between HDFC Ergo and ICICI Lombard.

Would love to hear from anyone who’s been in a similar situation or has insights into how this works behind the scenes.

Also, assuming the prices are almost equal - which one is better between the two? I checked previous posts and noticed slightly more complaints against ICICI Lombard than HDFC Ergo, but both seem to have their share of negative experiences. Are there better options?