IMHO, this is just another of the stories made up by Austen fans or non-fans who want Austen to have her own love story. The one above sounds a lot like one I heard once about JA and a "seaside gentleman," whom (who? grammar issues) she met on the beach and who later died.
(Syrie James wrote a novel about Jane and a possible romance, "The Lost Memoirs of Jane Austen." It's mostly accurate except for the entire basis of the book...)
I don't think it's likely that JA had absolutely no romantic encounters. How else would she have written about love and marriage and romance?? But, as she obviously never married, stories like the "seaside gentleman" and Francis Doyle's are most likely made up by people who want to think Jane didn't live a life without love.
I'm not saying that it's impossible Jane fell in love with Tom Lefroy, assorted seaside/naval gentlemen or anyone else. But I think it's a little absurd to say that she used some people in her stories. How does Sir Francis Hastings Doyle know that she wrote about this naval person, and how does he know that she used him as the model for Wentworth???
I think it's perfectly possible. But I also think that the above story, and others about JA's love life, are mostly made-up.