That's not entirely true. It depends what the state, local or tribal jurisdiction includes under the term "hate crime".
A "physical injury" can result from verbal attacks/abuse. That's already been proven in the courts.
You are correct, but all the federal parts of the law deal with assault, arson, murder, and so forth.
So for the enhanced funding and prosecutorial help to be used, the crime has to be one of physical violence. Maybe you can claim physical injury if someone yells an insult at you, but that would depend on the judge. This means that if a homosexual yells GO HOME BREEDER to me, I can invoke this law?
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(2) OFFENSES INVOLVING ACTUAL OR PERCEIVED RELIGION, NATIONAL ORIGIN, GENDER, SEXUAL ORIENTATION, GENDER IDENTITY, OR DISABILITY-
(A) IN GENERAL- Whoever, whether or not acting under color of law, in any circumstance described in subparagraph (B), willfully causes bodily injury to any person or, through the use of fire, a firearm, or an explosive or incendiary device, attempts to cause bodily injury to any person, because of the actual or perceived religion, national origin, gender, sexual orientation, gender identity, or disability of any person—
(i) shall be imprisoned not more than 10 years, fined in accordance with this title, or both; and
(ii) shall be imprisoned for any term of years or for life, fined in accordance with this title, or both, if—
(I) death results from the offense; or
(II) the offense includes kidnaping or an attempt to kidnap, aggravated sexual abuse or an attempt to commit aggravated sexual abuse, or an attempt to kill.
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It also includes “disability”, so if you look at the fed disability laws, anyone covered under ADA is protected under the law- and it goes way way beyond wheelchairs, crutches, and braces.