Portsmouth had one season in the Premier League in these nine, 2009/10, and eight outside it. It was the season they became the first Premier League club to enter administration, on 26 February 2010. They were docked nine points and went down in April. Burnley and Hull went down with them.
Take Manchester City out and almost nothing changes. Portsmouth lost 1–0 at home in August and 2–0 away in January, so no points come off. The deduction stays in the rebuilt table too. 19 points, 20th for real, 19th of 19 without City: City’s place and nothing more, fifteen points short of 16th.
The site’s 2009/10 page asks whether nine points relegated Portsmouth. It is a question about the deduction, not about City. Two defeats by City leave the rebuild nothing to take away.