The fact that the agent saw L=0 for IAH-BWI is typically a symptom of the fact that when looking at availability for each individual flight segment (but not necessarily booking it as you go), the inventory management systems don't have full visibility of the entire journey.

When the complete journey is booked and priced, all info necessary for the computer to recognize the trip as SJC x/IAH BWI is present and an accurate availability calculation can take place.

Just looking at availability for each distinct segment will reflect local, point-to-point status and it sounds as though on that basis, the IAH-BWI segment alone is not offering L class for sale. If that's the case, the computer is blindly unaware that the request for IAH-BWI is the second segment of an SJC-BWI trip. As far as I know, UA's availability systems will not split a 'direct' flight with a change of gauge into two unique flight segments with the same number, so the agent would have needed to look at each segment independently to achieve what the OP had asked for.

What is strange though is that .com should have the same journey context available to it as part of its multi-city search.