No, it actually sounds like a mess.

What the OP is describing is plating two separate tickets inside a single reservation. This is possible; travel agents are asked not to do it, but there's nothing preventing it. The problem is, OP does not have a ticket from MNL to DEN. OP has a ticket from MNL to LAX and then another ticket from LAX to DEN. OP asked UA to change to the nonstop flight, but there's no coupon that can cover the NRT-DEN flight because that ticket ends at LAX.

This is why UA is asking OP to contact the travel agency to complete the rebooking process.

I concur that any document that suggests you have an onward connection will get you through NRT security, but I'm not sure that the UA transfer desk is going to be a very pleasant experience. They can put you on the flight, but they may not know how, and it's likely a policy violation, and NRT isn't the station where I'd want to ask employees to make exceptions.