Hours after accepting a beer in an open cup from a stranger at a San Francisco road race in 2010, Heather Marlowe woke up in an unfamiliar home, vomiting and in pain.

Believing she had been drugged and raped, Ms. Marlowe called the police and went to the nearest emergency room. A nurse performed a “rape kit” — a lengthy, invasive exam that involves the collection of saliva, blood, semen, hair, skin cells, clothing, and other evidence from the victim’s body that is then sent to the police.

Ms. Marlowe initially was hopeful that police would apprehend her attacker. After several months, however, she learned that her rape kit had never even been tested.

In 2016, she sued San Francisco, claiming that the police department’s failure to investigate was part of a pattern and practice of neglecting sexual assault cases. Last month, she asked the Supreme Court to revive her case, which was dismissed by lower courts on statute of limitations grounds.

The crux of her argument is that, by deliberately deprioritizing rape investigations (the vast majority of which are committed against women), the police department unconstitutionally denies women the equal protection of the law.

Ms. Marlowe is not the only woman to sue to get police to take rape seriously. The New York Times reports that women in at least seven jurisdictions have filed lawsuits to force police to investigate their assaults.

Yet press attention tends to focus not on police inaction, but rather on the so-called rape-kit backlog. The number of untested kits indeed is large. According to the Atlantic, nationwide “as many as 200,000 rape kits sit unopened in police storage.” The real problem, however, is not lack of resources but lack of will.

Many of these kits are not “backlogged” at all, but have been discarded, forgotten, or put in storage by departments that have no intention of testing them.

The truth is, rape cases require an enormous amount of investigation. Many departments do not assign sufficient staff to sex crimes. Others simply walk away from tough cases. For her part, Ms. Marlowe says that a San Francisco police officer explicitly told her that the department was prioritizing “more important crimes,” even as it continued to focus on low-level nonviolent offenses such as vandalism and drug possession.

Ms. Marlowe regards the rape-kit “backlog” narrative as dangerous, because it allows police departments to escape blame. It also allows politicians to say that they are addressing the problem by throwing money at it.

Vice President Biden, now a Democratic presidential candidate, likes to take credit for the first federal rape-kit law, the 2004 Debbie Smith DNA Backlog Grant Program, which distributed more than $1 billion in federal money for rape-kit testing.

Despite these grants, though, hundreds of thousands of kits remain untested, and nationwide clearance rate for rape cases remains shockingly low, at approximately 40% — with some cities posting clearance rates in the single digits.

Nevertheless, politicians and activists continue to claim they can solve the problem — if only they had more money. Another Democratic presidential candidate, Senator Kamala Harris, says she wants the federal government to spend another $1 billion on the “backlog.” State and local governments are handing out rape-kit cash like candy. (In Massachusetts, the supplemental budget recently signed by Governor Baker allocates $8 million for the collection and testing of rape kits.)

Ms. Marlowe says that “reauthorizing funds for testing won’t bring justice to rape victims until we address the problem of law enforcement’s policy choices when it comes to investigating rape and sexual assault.”

Whether Heather Marlowe’s legal claim succeeds remains to be seen. She faces not only procedural but substantive hurdles, since courts generally give police departments wide leeway to set priorities.

Irrespective of the legal outcome, Ms. Marlowe has brought needed attention to the failure to prioritize rape investigations. As with so many social ills, money will not solve this problem. But a change in priorities might.

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Ms. Braceras is director of Independent Women’s Law Center. This column first appeared in the Boston Globe.