Technically speaking, the agents are right. If you route a through fare across multiple flights, UA can arbitrarily adjust the inventory by adding or removing from what you would "normally" expect from taking the set intersection of each segment. This is called "married segment logic". It can work both ways - adding availability that is not present on one or more segments, but in this case it's working against you.
The through fare availability is
Code:
F5 A5 JN5 C5 D5 Z5 ZN5 P4 PN2 R0 RN0 IN0 I0 Y9 YN9 B9 M9 E9 U9 H9 HN9 Q9 V9 W9 S9 T9 L9 K9 G0 N0 XN0 X0
If you want this itinerary at the saver level, you can exploit a loophole in UA's booking engine. If you use multi-city search, the engine will apply the broken-up inventory but apply the through fare. So you should be able to book this itinerary online by doing a multi-city MIA to IAH, IAH to CHO and selecting your flights.