It does. I typically combine data from Google & Bing WMT as well as Majestic SEO and OSE when researching backlinks. I don't subscribe to Ahrefs.
Majestic is probably my favorite source as it tends to show the largest sample and provides a lot of additional info that the others don't like image vs text link, follow vs. nofollow, if image then alt attribute values, etc.
Majestic does the latter (filters out deleted links)... unfortunately, no one crawls as many web sites or as crawls those sites as deeply as does Googlebot. And the resources (server power, disk space, electricity to run the servers, etc.) that would be required to do so and to maintain just link graph data (no content) equivalent to theirs is mind boggling.