I can only give my opinion, I'm not a lawyer but employ them and my company runs contracts on minimal paperwork, you can be contractually bound by a phone call these days and that includes insurance cover.
I'd say as long as it's a good company and *you know it is* you swipe your card and sign contract so are under contract and therefore the insurance agreed is applied. It is a quick as swipe, sign and go, contractual obligations will apply both ways.
For car hire I can only speak for my Lesssaggro experience, I've never been concerned about studying the small print and filling the forms at airport, a run through and complete next day in their office is fine and a great service if staying in Nerja. Also I've never had a problem dropping the car at the airport unchecked, they are an honest company and not going to claim for damage you haven't caused IME.
it's all about using good companies you can trust, trust actually still works in business, it's fundamental to my business organisation and something many companies and punters chasing lowest prices appear to lose sight of in the general rat-race of car hire quotes IMO.