Not even a rios fan but i dont know of any drug/blood test that is conducted by having the sample put in a glass cup.
In one of Elie's videos, you can see the VADA officials taking samples from Rios during a training session with their containers and other materials sitting on the edge of the ring. Obviously that's a far from sterile environment, considering the ring's surface can contain other bodily fluids like sweat, saliva and even blood from the multiple training/sparring sessions at the gym. It makes you question their testing protocols.
I didnt see that part but no. The specimen container can sit wherever they wanna put it as long as the seal is tact.