At this point you have identified an uncertain father (Jonathan) and FindaGrave has identified a different father (John). More research to flesh out these two persons could be useful in identifying whether Solomon was in fact the son of either.
I went ahead and edited Solomon's profile in chronological form in order to group together information about the same topic (his marriage) which had been scattered. This required using the form <ref name="arbitrary site identifier"> in order to cite the same source but with information now scattered through the profile. I think you'll find use of this form helpful as you continue your research. In addition, when you obtain conflicting data-- as you already have, with his parents, it will help answer the question, "which source provided this information, and which of the competing sources is the more reliable?"
This is one of the tragedies of the Find a Grave site -- it would be so easy for them to require sources but they don't. So their naming a John Barrett is something to consider -- and they have a nice profile for him, a Revolutionary War soldier -- but that can only be a starting point for further research to figure out why they made the connection, or whether they got it wrong.