It's somewhat more nuanced than that. The currently approved swabs have limited availability, and indeed there are others (unapproved) that would work. However

It's somewhat more nuanced than that. The currently approved swabs have limited availability, and indeed there are others (unapproved) that would work. However it seems you can't use just any - they have to consist of synthetic fiber, can't have a wooden shaft, and can't contain calcium alginate. This rules out many of the swabs that a healthcare facility might have on hand. (https://khn.org/news/as-coronavirus-testing-gears-up-specialized-swabs-running-out/ https://khn.org/news/as-coronavirus-testing-gears-up-special...)