Lawyers and law firms get to have it both ways. If you are a client of any lawyer in any firm, all the lawyers in that firm get the privilege. But, if there is a conflict of interest they will still take your money and just assign it to a different desk.
It actually doesn't work this way in business. I worked for a company and when we had to defend something involving intellectual property, our IP lawyer still had to check that there was no litigation conflict of interest. If there was they would have to recuse from the case. The case settled pretty quickly if that matters but my point is, if there is a conflict there is a conflict throughout the office. I guess some pigs are more equal than others.
And the fatter the sow, the more “equal,” it seems.