"..... so it can call the shots on its own legal defense."
If an insurance company funds the defence, and is liable to pay any damages awarded, the insurance company calls the shots.
There can sometimes be a conflict of interest between the insurer and the insured.
An insurance company takes a 'business' view when there's a claim.
ie How much will it cost us to fight the claim compared with how much will it cost to to get rid of the problem by paying off the claimant - often regardless of the merits of the claim.
Even if the insurance company makes a payment expressly without admission of liability, it will almost inevitably be interpreted as an admission of liability by the manufacturer.
In contrast, the manufacturer will wish to protect its reputation and, not unreasonably, sees anything which will be interpreted as an admission of liability as damaging to future sales - often preferring to fight and lose rather than admit liability (except in clear cut cases.)
eg A few years ago, I represented a major 'household name' aviation equipment manufacturer in a claim by a small airline following the crash of a commuter airliner in which all crew and pax were killed. The claim, for the loss of the aircraft and loss of life of the crew, was £3-4 million. I considered the claim was ill-conceived and that our prospects of successfully defending it were good. However, the insurer took a 'business view' and instructed us to make the claimant a 'without prejudice' offer of £0.5 million. The manufacturer was extremely unhappy because of the potential long term (and unjustified) damage to its brand name but, because the insurer 'called the shots', had no control over the conduct of the defence.
In the event, all ended well because the claimant rejected the offer and we went on to win - with the claimant being ordered to pay the manufacturer's costs of defending the claim.