Yes, FIP will work on both HEx and Heathrow Connect. HEX joined the staff travel scheme about 10 years ago.
I'm not sure where you've heard this from. HEx staff don't get access to FIP (only ATOC) so I can't see why there would be an agreement to accept FIP.
Up until last year I worked in HEx ticket offices and am quite sure I remembered our Ticket Recognition Guide stating that we were not to accept FIP or PTAC (London Underground staff travel card). In fact I just managed to access the Guide on our Intranet and it definitely says no FIP / PTAC.
ATOC is acceptable for HEx provided you buy a ticket from a ticket office before boarding the train and gets you the usual 75% off the fare. Free boxes cannot be used.
Where it gets complicated is with Heathrow Connect. Whichever staff passes FGW accept are valid between Paddington and Hayes & Harlington (including free boxes on ATOC). Beyond Hayes the more restrictive HEx arrangements apply as above.
Hope this helps.