No. Once the drug has assimilated into the body there is no longer possession. A drug test alone would not be sufficient. However, a drug test could be circumstantial evidence of possession and be used to bolster the testimony of someone who witnessed a defendant in possession prior to swallowing the drug. Possession is illegal in both private and public locations and is irrelevant to a controlled substance charge.
Assuming that when you say "having a controlled substance in the body" you mean in the blood (as opposed to drugs that were swallowed in a protective wrapping for transportation purposes) than Mr. Lawrence is absolutely correct. No charge can be brought simply for having a positive drug test. Furthermore, it does not matter whether or not you were in a private or public location since possession of controlled substances is illegal regardless of your location.