It also says "V fare basis" at the very top.

I'm not sure what you're referring to when you say "you kept asking for the cheapest price". Who did you book the ticket through? I work for a giant company..there's nothing magical about the discounts..the travel agency doesn't do any searching for lower prices. They're negotiated..we've got them on AA, DL, UA, WN, and some foreign carriers... we have one travel agency we use for booking and I have to go through an interface called Concur to book..I pick my flights through that and the agency tickets what I've chosen (or I can call them for a more complex itinerary..for a higher booking fee). There are no bulk fares.

Now... if you book through an agency and then try and change your ticket directly with UA they may refer you back to your agency to make changes..that is quite common (unless it's the day of the flight for an SDC, during IRROPS or after travel as begun)..perhaps that's what you encountered. In fact in some cases they'll charge a $50 "ticket takeover" fee to assume the ticket from the travel agency and then make changes. I've never been charged that as a 1K..but I know others who have. Delta and American also do this for travel agent booked tickets..quite annoying.

That's a column header, not an indicator of the fare basis being V.

Not necessarily. In the "bulk" situation referenced, iflyuaaa's employer may use a corporate TA which purchases bulk seats as part of its offering and then makes those available to its clients. In effect, the TA is a wholesaler, not a TA.

UA can't take over or otherwise touch those tickets because it does not even know what the passenger paid for the ticket (UA sells at a discount and the wholesaler sells at a markup which still represents a discount).

This is a huge PITA for the employee, carries other significant problems such as SDC, earning and the like, but it may represent major savings. So, it's there.