It’s fine to call it user testing
This linguistic canard does the rounds every few months, and UXers’ erroneous vehemence about it isn’t… healthy.
In the phrase ‘user testing’, the word user is a qualifying noun, also known as an attributive noun, or adjunct noun. As the name suggests, it modifies the second noun. (Here, testing is a gerund, a verb acting as a noun.) But that modification can have multiple meanings. Sometimes it implies of, but it can also imply, say, with, by, or for. Some languages add extra words for these distinctions; in English, we rely on the context to make it obvious.
‘Mobile design’ does not mean designing mobiles. It means designing for mobile.
‘Charcoal drawing’ does not mean drawing charcoal. It means drawing with charcoal.
‘Customer feedback’ is not feedback on customers. It means feedback from customers.
In 20 years, I’ve never met a client or colleague who thought ‘user testing’ meant actually testing users. Maybe you have. If so, my sympathies: your project likely faces problems more serious than this labelling issue.
There are a thousand more meaningful battles to pick, folks, and you might even be right about some of them. Let this one go.