No. If you read them carefully, the sources and their examples are somewhat ambivalent. You can use them as general guidance if you want, but they do not cover all contexts and uses. You have seen the examples in #48.All grammar sources say it is incorrect.
These sound wrong to me. But "training" is a noncount verbal noun, so "during training" is fine (unless the context makes it like "during dancing").Dance Etiquette For Beginners | realbuzz.com
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Errors inevitably happen during dancing and they should not spoil the occasion.
Sevillanas - Wikipedia
"Turning during dancing" (picture title)
Ok, why then there is no "the" like, I believe, there should be when we talk about a training session at work?In case no. 4, it is perfectly correct to use the word during, e.g: He was injured during training (noun).