It's not that. It's that people who don't think he's guilty are telling him to stfu because it makes him look bad.
For example you ask me if I murdered someone and I respond,
is much better than
"I'm sick of questions like this, it's annoying, it ruins my routine I wish you'd just leave me alone"
every single word he utters on the matter makes him look worse. The best way to handle it was how Brock Lesnar did, saying no and then not talking about it more, made him seem not guilty.
Well..., assuming the fact he never once said anything about the test themselves, only how and when they are taken, you example is stupid.
A less stupid form of your example would be, midday during your free time, you are questioned, "Did you murder someone?" You answer calmly and politely, "Nope."
You are woken up early in the morning, "Did you murder someone?" "No I didn't ******* murder someone! Why the **** are you bothering me with this dumb shit? Leave me the **** alone!"
To summarize, being annoyed or pissed off by the timing of something does not mean you have a problem with that thing in itself. I'm willing to bet that if they would've brought him in for testing during lunch or after, he'd have no problem with it.