Isn't every supermarket plastic bag easily punctured by a finger?
Depends on the size of your fingers.
Indeed, the rule for recycling what is called "
Film" here (and I provided a link to our local recycle group of which I volunteer) is IF you can push your finger though it, it can be recycled in the appropriate area. For us, that happens to be at our local supermarkets. So
yes, is the answer to your question.