She did write "Farpoint" herself. She wrote the original 90-minute version of the pilot, the part involving Farpoint Station, the Bandi, and the space creatures. When the decision was made to expand it to 2 hours, Roddenberry tacked on the Q subplot to pad it out -- which is why Q has no actual impact on the story after they arrive at Deneb IV, but just pops in occasionally to kibitz. So 3/4 of the pilot is Fontana's, which is why she got top billing in the writing credit. ("Written by D.C. Fontana and Gene Roddenberry," the spelled out "and" indicating that they worked on separate drafts. If two writers work as a team, "&" is used instead.)
Normally, co-writing the pilot would mean that Fontana was entitled to co-creator credit for the series, but Roddenberry campaigned to deny her credit. That's what she was probably annoyed by.