That method confuses me also
Although now, it seems that most every tire store chain is told to do both
No one uses what are called HOT Patches any more, they were mostly used on tire tubes
The theory now is, if you place a patch on the inside of a tire, water can still enter through the exterior hole of the puncture & therefore have access to the metal banding in the tires core & over time rust that metal. Rust would cause separation of the metal bands & the rubber
Plugging would fill the puncture hole & keep water away from the metal bands
?? Possibly the patch on the inside keeps water/moisture from entering the puncture from the inside, therefore again protecting the metal bands ??
Air that comes from a compressor would always have a small amount of water & compressor oil in it, even if you have a water separator in the line, that may be why everyone seems to be pushing the use of Nitrogen in the tires