I wouldn't say go with gut feeling particularly, but rather follow all the evidence you possibly can, until something comes up to counter it.
In this case the lead you had was that he said he was born in Farningham in 1785.
So, following that, you are led to someone with the right name, right place , right year.
So unless there is any reason to suppose this isnt him (most likely scenario being there are others with the same name in the same place at about the same time, and you have homed in on the wrong one - but you can check that out easily) then no more is needed.