SHARES is a really awful interface. It also shows the most logical (read: shorter) connections first.

So when searching ORD-MEX, the later ORD-IAH-MEX will show up first. They will have to do some digging to find the earlier ORD-IAH connecting to the same IAH-MEX.

If you get them to break it up (look at ORD-IAH, now look at IAH-MEX), then they'll find it.

I wouldn't say the agent is lying, rather they don't have the tools to efficiently find what you want, so misinformation runs rampant at the new UA, so I would try to brush off any sort of anger -- this is quite normal with COdbaUA.

I had one today where the agent told me my IST-SFO trip I was attempting to book would not confirm upgrade. I pointed out that there was upgrade space on IST-EWR and EWR-LAX, but not LAX-SFO (that was the segment that was causing the problem). She was only trying to be helpful by cautioning me that if I bought this ticket, I wouldn't clear, and she was using the information that was provided to her by the computer (R0 when searched IST-SFO). She was an experienced agent, and helped me book this ticket. But the tools she had didn't show her what was important (I'd clear IST-EWR-LAX immediately, which was the majority of it).

She wasn't lying, rather, the tools are so bad, it takes a lot more effort to find accurate answers with UA these days.