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Snopes says her methods are legit

Rubin says she is certified on a device known as a handheld XRF, or X-ray fluorescence spectrometer. Such a machine is used extensively in a variety of scientific disciplines and can provide a basic assessment of the chemical composition of an object by exciting the object’s molecules with X-rays and seeing what secondary X-rays are emitted, according to Thermo Fisher:

XRF analyzers determine the chemistry of a sample by measuring the fluorescent (or secondary) X-ray emitted from a sample when it is excited by a primary X-ray source. Each of the elements present in a sample produces a set of characteristic fluorescent X-rays ("a fingerprint") that is unique for that specific element, which is why XRF spectroscopy is an excellent technology for qualitative and quantitative analysis of material composition.

Experts agree that this method is a valid first approach for the detection of lead in a sample. A 2013 study performed by researchers at the California Department of Public Health Childhood Lead Poisoning Prevention Branch suggests that XRF “is an effective screening method for food and similar items with lead content > or = 10 ppm [parts per million], provided the operator is trained to identify lead spectra.”

We reached out to an expert via email: Howard Mielke, a professor of Pharmacology at Tulane’s School of Medicine, who heads a research unit into lead contamination and once served alongside Rubin as a board member for Lead Safe America. We asked him if XRF was a valid method for Rubin’s purposes, and he told us that it was, but only as a first step. The second and more expensive step involves seeing how much if any of that lead is capable of being transferred to a child: "The use of the XRF is suitable as a first step in determining lead in an object. The second step involves evaluating whether or not the lead is readily picked up on hands or ingestible through the use of the object. The second step is the expensive step but it provides information critical to understanding the possibility of lead poisoning from the object."

Note that the story here says the toothpastes have lead in them, not that they're necessarily causing lead poisoning, so it seems entirely accurate.

Shame on the Guardian

They're not the only ones reporting this,

https://fortune.com/well/article/toothpaste-brands-toxic-metals-lead-arsenic-mercury-cadmium/

https://gizmodo.com/a-new-report-suggests-we-all-may-be-brushing-our-teeth-with-lead-and-other-toxic-metals-2000591000

https://www.hindustantimes.com/world-news/us-news/popular-toothpaste-brands-contain-dangerous-heavy-metals-new-research-finds-101744975079972.html