I think you were given duff information. If you take a look at this thread in the 5X forum you will see comments indicating the Garmin engineers are working on a Strava live segments problem and have it working themselves. And as Crispin indicates, some people have it working just fine.
https://forums.garmin.com/showthread.php?372020-fenix-5X-frozen-gt-Garmin-triangle&p=959804#post959804
Nope, my GC segment tab only shows Garmin segments! Uhg
Wow. I think I finally got it. I had to use Garmin Connect on my iphone to go to my segments and then chose Strava. It wouldnt let me do it on my PC. Now when I try to see segments on GC via PC, it just says "use Strava to look at your segments, you are using Live Segments". I think I got it now. My F5 is syncing and its taking a long time, so I presume its syncing all those segment FIT files. Thanks!!
Ran yesterday with mine and Strava segments popped up perfectly! Awesome!!
They were working fine for me on two runs over the weekend; including a in run notification that you are approaching a starred segment and a 'special' segment datafield screen when in Segment. Have you checked that segment alerts are on in the run app settings? Also worth checking the GARMIN/SEGMENTS folder on the watch when plugged in to a PC/Mac to check that the segment files have been sent to the watch.