I've read a lot of methods of valuation for public companies. One striking consistency I've seen recently even among professional writers is comparing U.S. companies PE ratio, forward or trailing to the S&P 500 or the market.

I don't think PE is the greatest ratio for determining value. I don't think any ratio alone can find the intrinsic value of a company but it can be useful to get a ballbark idea in some cases. Having said that it would seem more usefull to compare the companies PE or price to free cash flow, EV to fcf/ebit etc. to another company in its same industry. This company competes next to it unlike the overall market with thousands of different companies with different
products,services,accounting,growth prospects and so forth.

Maybe they are making the case that the S&P 500 could be your opportunity cost so why invest in this company with its current valuation when you can buy the market for cheaper through a fund or etf. An investor should always consider opportunity cost but I don't see the logic in this comparison because the US economy and Large-Cap stocks have very different prospects and barriers than say one single company. Say the company has a pe of 10 and the market is 20. Who knows what the market is going to do. The FED may not even know. Say the company grows at 2% a year and the market 15. This has to be taken into account as well. The companies ability to compete and maintain revenues among many other measures seems more important than a simple valuation ratio comparison to the overall market or index. In fact, it seems out of place.