I think when you say 'match', you're actually looking for a color that will compliment the rust colored rug; not 'match' it, correct?

This link may give you some ideas - Complimentary colors for rust

One of the neutrals we use is SW Nomadic Desert. Looks good with earthy tones. The swatch looks pretty dark but it looks more mid-tone once on the walls. Would not paint anything on the walls until trying some samples. Take some sample boards and find 3 to 5 colors you like. Paint a color on each board and look at it in the room at different times of day.