What fees actually get charged are somewhat up to the whims of the agent checking you in, especially because the baggage policies on the web are not always written in an unambiguous manner. From my reading of the United policy (in italics below), it seems like you won't be charged both a oversize and overweight fee. But my reading, or the interpretation of the "rep" you talked to, is completely immaterial. It only matters what the agent who checks you in thinks. And that may depend on how much sleep he got the night before, what he had for breakfast, and how nice the passenger in front of you was to him.
United accepts non-motorized bicycles with single or double seats (including tandem) or up to two non-motorized bicycles packed in one case as checked baggage. If the bicycle(s) are packed in a container that is over 50 pounds (23 kg) and/or 62 (158 cm) total linear inches (L + W + H), a $150 USD/CAD service charge applies each way for travel between the U.S., Canada, Puerto Rico and the U.S. Virgin Islands, and a $200 USD/CAD service charge applies each way for all other travel. If the bicycle(s) are packed in a container that is less than 50 pounds (23 kg) and 62 (158 cm) total linear inches (L + W + H), there is no bicycle service charge, but the first or second checked bag service charges may apply.
Having said all that, there's no way I'd fly United with a bicycle, not as long as there are still bicycle-friendly airlines such as Frontier and Southwest around. Note that it should be fairly easy to meet the 50-pound restriction, and fairly impossible to meet the 62-inch restriction.