As you say, Breitbart have often reported on Burke. In April 2014, for example - just a few months before the Institute's conference in Rome - Burke was a guest of Bannon's on Breitbart News Sunday. It is a very strong "connection".
And - again as you agree - Burke is a senior man in the Institute.
All the facts support the suggestion that Burke would have been involved in inviting Bannon to speak to the Institute in 2014.