See source: http://fmg.ac/Projects/MedLands/FRANCONIA%20(LOWER%20RHINE).htm#Bur...
It says at the above source (about his parents):
"[Three siblings]. Parents not identified. Burkhard [IV], son of Dietrich [III], was named after his paternal grandfather. If the same naming pattern was applied in earlier generations of the Broich family, Burkhard [III] could have been the son of Dietrich [II] who is named above."
and further down:
"Burkhard [III] & his wife had nine children:" with a link to http://fmg.ac/Projects/MedLands/FRANCONIA%20(LOWER%20RHINE).htm#_ft...
Other than Dr. Eike Pies publication I can't find any proof of Goswin I. being an illegitimate child of Burkhard III. - does anyone have a more credible source?