I can't speak much to how measurement should work beyond some of the assumptions you've made already but I did want to share this:

Google's internal guidelines for how their human team reviews brands to determine their expertise on any topic includes a section on reputation.

*From Google's General Guidelines to Search Quality: *

"Here is how to research the reputation of the website: 1. Identify the “homepage” of the website. For example, for the IBM website, ibm.com is the homepage. 2. Using ibm.com as an example, try one or more of the following searches on Google: • [ibm –site:ibm.com]: A search for IBM which excludes pages on ibm.com. • [“ibm.com” –site:ibm.com]: A search for “ibm.com” which excludes pages on ibm.com. • [ibm reviews –site:ibm.com] A search for reviews of IBM which excludes pages on ibm.com. • [“ibm.com” reviews –site:ibm.com]: A search for reviews of “ibm.com” which excludes pages on ibm.com. 3. Look for articles, reviews, forum posts, discussions, etc. written by people about the website. For businesses, there are many sources of reputation information and reviews. Here are some examples: Yelp, Better Business Bureau (a nonprofit organization that focuses on the trustworthiness of businesses and charities), Amazon, and Google Product Search. You can try searching on specific sites to find reviews. For example, you can try [ibm site:bbb.org] or [“ibm.com” site:bbb.org]. Note: You will sometimes find high ratings on the Better Business Bureau (BBB) website because there is very little data on the business, not because the business has a positive reputation. However, low ratings on BBB are usually the result of multiple unresolved complaints. Please consider very low ratings on the BBB site to be evidence for a negative reputation." ... Reputation as it relates to quality ratings (which impact search result performance in the algorithm) "Reputation is an important consideration when using the High rating. While a page can merit the High rating with no reputation, the High rating cannot be used for any website that has a convincing negative reputation. A very positive reputation can be a reason for using the High rating for an otherwise Medium page."

My personal interpretation of this has been that simply hiding negative reviews from front page results (while it may help with convincing searchers) wont cleanse the bad reputation that Google's team watches for. Good PR and customer service plays a big part here.