As said above, if the guy said there's a risk of a blowout, then perhaps the nail is in the sidewall?
I had never thought about using an innertube; :beer: to the person suggesting it. I've tossed a few tires over the years but, now I'm convinced an innertube may have saved me a couple pairs of tires.
Also, you can get the plug kits for a few bucks from an automotive parts store; they're about $5. A bike pump (or cigarette lighter pump) and a plug kit in the trunk will sometimes save you time over putting on a spare tire. However, if you have road-hazard coverage; some are voided unless you take the tire to a service place and have a patch put inside.
I once had an exhaust pipe-clamp puncture a tire. It had been sharpened (apparently) by being dragged on the ground under someone's car until it finally broke off. What I thought was a nail turned out to be a long curved hunk of metal. My tire had just gone flat about a block from a gas station, so I drove to the air pump. After it was pumped up, I heard a slight leak - seeing the piece of metal, I grabbed it with some pliers, pulled it out, and the tire went completely flat in about 1 second. 1am, 25 miles from home; I put what I thought was a temporary bandaid on it- it took 3 plugs to fill the hole. They lasted the rest of the life of the tire.