Many red flags. The familysearch profile for "William John Pagett", leaving aside the fact that nobody used middle names at that time, has 2 sources, one about a Thomas Pagett in Rothley, Leicester in 1501 and one about a non-conformist Thomas Pagett in the latter half of the 1800s in a totally different place...nothing about a William or a John let alone a son Richard....it's a sad example of the kind of garbage that gets thrown into familysearch profiles with no thought or oversight.
My advice would be to start with the existing WikiTree profile which needs improvement drastically (maybe some of those sources are actually OK but they aren't associated with specific facts, don't have links etc so it's hard to tell at first glance) and work from there. Find records at the UK national archives or in visitations free on archive.org etc, flesh out that profile to try and find verifiable information about the man and his family. Then you may be in a position to make a supported assertion about his parentage.
Best of luck!
