Roadside assist fixed a punctured tye with a plug. Repairers can't find a leak. Safe to keep driving?

I had a punctured tyre over the weekend. The cause was a bit of fencing wire, about 2.5mm in diameter. Roadside assist plugged the hole with this gooey looking strip of... something. Threaded it onto a giant needle, pushed it into the hole entirely, pulled out a portion of it and trimmed off the excess plug, and told me that it was enough to get me home, and to take it into a tyre shop to get it repaired.

Took it into the tyre repairers this morning and they said that they couldn't find a leak and didn't perform any repairs (didn't charge me either). Apparently, they dunked it into a tub of water and there were no escaping bubbles.

When I explained the plug, they said that's what they would've done too. Sooo... is it safe to keep driving on the plug solution? Or should I go find another shop and insist on a 'fix'?