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In the USA either my doctor takes the blood, or in certain cases, they have Labcorp or similar do the test (I asked and it was because they didn't have the proper vial labels to do the blood test in house). I also get copies of the test and it has the logo of the testing company.

So yes

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It works both ways. I walked into the Theranos and volunteered for bloodwork. I’ve also had my doctor send my bloodwork order to a lab of my choosing when I’m e.g. traveling.
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