Thanks a lot for your question.  The answer is no.  The environmental performance of companies is based on many measurable "metrics" or key performance indicators. For example the most common ones in our sector are:

Greenhouse gas emissions

Emissions to air

Emissions to water 

waste to landfill

Forest certification and chain of custody

Each one of these can have several parameters that companies measure.  For many leading companies you will find the results in their annual sustainability report.

Using recycled fiber in paper is a small element of sustainability and is a choice of raw material.  It does not mean that the company is more sustainable or even that the paper grade has a lower environmental footprint.  The life-cycle of paper is more complex than that.

I hope this helps.