If you want to speak pure American English, you must study British English.

Assumption 1: You are exposed to both spoken American English and British English.
Assumption 2: You want to speak pure American English.
Assumption 3: You do not speak pure American English.

Conclusion: You have to study British pronunciation.

Proof

Notice that your input influences your output. In other words, what you hear is the basis for what you speak. This is because of the imitation-skill that you employ when learning pronunciation.

By Assumption 1, you are influenced in the direction of British English. By Assumption 2, this fact is undesirable for you. Hence, you need to guard against it. Metaphorically speaking, your British English input is your enemy, and you must know how to defend against this enemy.

One way would be to remove the enemy from your environment. But this is impossible by Assumption 1. So you need to be prepared for the constant existence of the enemy. You must be "immune". You must be so prepared, so vaccinated, that the existence of the enemy is harmless.

First of all, you must be able to recognize the enemy. If you do not see the difference between American input and British input, both kinds will influence your output, via the imitation-skill.

By Assumption 3, your knowledge of American pronunciation is incomplete. Hence, if you meet an unknown piece of input, it could be a missing piece of knowledge about American pronunciation. So you must not ignore it. You must study it. It can be American or it can be British. But you must absorb it only if it is American.

So if you want to expand your knowledge (which you do by Assumptions 2 and 3), you must have the technical knowledge to tell between American and British. So you must have technical knowledge about British pronunciation. Thus you must study British pronunciation, and the proof is complete.

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Let us try to challenge the conclusion that it is necessary to have the technical knowledge to tell the difference between British English and American English. Let's imagine someone saying, Maybe I don't need to see the difference. If I know a person is British, I can ignore what they say.

The defense of the necessity of such technical knowledge would go on like this: The phrases "to see the difference" and "to ignore what they say" are only phrases. We must make our discussion more precise. These two phrases suggest that the learner is conscious of the input, is aware of whether British or American is being spoken to him, and that he can decide to shut off the input and prevent it from entering his head.

We don't know if it is possible to direct the workings of one's mind in this way. The following scenario is dubious: The learner recognizes that her speaker is British and so she uses her free will to tell her mind not to absorb this speaker's input; and the mind obeys and this speaker's input is shut off.

It is more likely that the mind itself must possess the power to "see the difference" and to "ignore the input of one kind" and to "be influenced by the input of the other kind", leading to the conclusion that technical phonetic knowledge needs to be encoded in the brain.

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