I've heard this argument dozens of times and, quite frankly, I don't get it. How does putting their HQ in/around DC give them a stronger hand with the government?
DC has no representation in Congress, so if they locate within the District they will have 0 people with political power advocating directly on their behalf.
If they locate in VA or MD, they'll have those state's delegations but that's it. Which isn't any different than if they picked MA, GA, TX, etc.
Amazon already has power in DC. They bought the Washington Post and have a major lobbying arm. Putting a HQ office there will do nothing to increase that, Congress doesn't actually care about DC or the surrounding area!