With all due respect Mercy, this is not true. There is only one BG where this tactic is actually working and that would be Arathi Basin. The multiboxer cannot be at each base at the same time and capturing flags drains 5+ players time. However, this requires coordination to exploit and coordination in random BGs can be next to borderline impossible.
But aside from that there is no way to win a BG without dealing with the MBoxer.
In WSG the MBoxer will almost always grab the flag, so you got to deal with him sooner or later.
In EotS the sheer concentration of characters in a tiny space allows the MBoxer to capture bases far faster than the opposing side. The only hope is to either CC the MBoxer constantly on the roads and hoping he does not have team members dispelling him and/or going for the flag while he goes for bases.
Finally in AV the MBoxer can simply turtle at a choke point like Dun Baldar bridge or Iceblood/Tower Point path.
I personally deal with multiboxers with the most sinister and wicked tricks I know of that are legal, out of pure spite. Hence I will stay mum about them.
Alas a few tips can be given:
1. Focus on AoE CC as much as possible, and in a quick succession. For example, lob a grenade into the pack and then immediately use eg Shadowfury.
2. Identifiy the leader, but also the 2nd switch target. It is difficult, but this will make it easier to take the MBoxer down. If you know what char that is up next upon a switch due to death/CC, you can be one step ahead and hinder it.
3. Exploit the range. The MBoxers often needs to cast at long range or get in a bit closer to use instants. Exploit this weakness by being a pain in the neck with undispellable AoE slows like Improved Blizzard .
4. Depending on the multiboxer and your profession, use reflectors, the results are both spectacular and amusing.
5. While Mercy may be wrong about you not having to fight a MBoxer in a BG, you can still avoid the MBoxer to some degree. Most importantly however, take any chance you get to CC them with things like Sap, Blind, Polymorph etc.