Agree with John's points, above.
I am not sure I have ever heard of a person doing ANY non-waived Lab testing without having earned a degree specifically in medical lab science. Even with that, you would have to have passed a national board exam in the US. Possibly there have been people grandfathered under certain circumstances?
Regardless, the thing about training is, I can train a high school student to perform the steps to start a test or do routine maintenance in a Lab. But they would not have the education required to understand what "it all means", which is essential in pretty much any healthcare profession--especially one so technical as Lab Science.
You may, indeed, have earned credits in inorganic and organic chem, microbiology, etc, but if you look at a certified program for a MLS (or MLT for that matter) you will see that beyond basic biology and chemistry, there are a load of specific courses that must be completed as the professional part of such a degree. A general biology degree (or any other type of degree for that matter), whether AAS, BS, MS or PhD, does NOT qualify a person to perform most of the functions done by a Lab Tech.
Scott