The agent was flat out wrong. SDC does not result in any refunds if there's a fare difference. Taxes/landing fees are a separate issue but I'm not aware UA refunds those, either. Nor do they charge them when you add additional stops to your itinerary.

There are two ways to change your flight on UA when IROPS are not involved:
1. Use SDC which gives you the ability to move your flight up or back more or less 24 hours. Whatever fare buckets are currently open for the flight you want to get on is irrelevant as the ticket is not repriced during SDC. Your fare remains the same but you get on the new flights you want provided they meet the routing rules of your original fare. It's really that simple.

2. Pay the change fee for your ticket and get your flights repriced. This is usually not a smart move since the change fee is $150 or more and most flights won't price out at a higher refund rate. Plus, if you are changing the return portion of a roundtrip ticket UA uses the then-in-effect prices when you booked the ticket which means your new flight is not likely to cost that much less. Also note that if you do this for the outbound then your entire ticket gets repriced at current fare levels so you would need it to be at least $150 less than you paid to get any fare difference refunded.

Sorry, OP. You were given very wrong info from the agent and you should not be expecting any refund in the mail or in your TravelBank. Now, if you were to write to UA and explain the situation they may offer you a small token gift of some miles but I wouldn't even expect that.

-RM