I do not agree that these exceptions apply to Boston's situation. Unless the police had reason to believe that a specific home was endangered, they needed a warrant. Searching my home when I refuse permission does not fall under the emergency exception unless they have reason to believe that the terrorist is in my home, or that we are in danger of a specific harm if they wait for a warrant (thermal images, tracking dogs, or some other indication that my home faces a unique and individual risk). The police do not have authority to search every home in Boston simply because there is an armed and dangerous criminal in Boston; they need something more, something specific to the home to be searched without a warrant. Otherwise the Bill of Rights is dead, and we have moved to a world where the law is whatever those in power say it is, in other words, a world without law.
Well, your agreement or disagreement won't change the outcome of what took place in this case, or any future one where exigent circumstances (hot pursuit) takes place.
This is not the first time such pursuit has taken place, and it won't be the last.
Bottom line, it's constitutional, it's legal, it'll take place again in the future. People won't like it, but they have little recourse to 'the law' - as it is already deemed 'in their favor.'