The most reliable way to increase search engine traffic is to create great content that your audience is looking for. For example, if you’re a pest control company, you may write a bunch of quality blog posts on getting rid of pests. The idea is to educate your prospects and move them towards buying from you. This is exactly where SEO intersects with content marketing.
As pointed out, they are certainly not the same, but it might not be a bad idea to track and report on the direct traffic. If there has been outreach done and the company is mentioned in print with a URL, direct traffic (along with some search traffic on the URL or business name itself) is likely to go up. If your email newsletters are not tagged, they're likely to show up under direct traffic. Depending on your role, some of what you do under the greater SEO/inbound marketing role can show up under the direct traffic.
Although it may have changed slightly since BrightEdge published its report last year, the data still seem to hold true. Organic is simply better for delivering relevant traffic. The only channel that performs better in some capacities is paid search ads, but that is only for conversions, not overall traffic delivery (Paid Search only accounted for 10 percent of overall total traffic).