I had the same experience last year. I was told they did a group thing where everyone had to get up one at a time and tell the group their name and something else and when she got up she started crying. The 'teacher' was very "yeah, so we decided that we had to do that activity more to get her better with speaking to a group"
Uhm, I'm sorry, she's 3 (well 3y7m now) perhaps she's just a naturally shy child, which she is and has always been. If she would have been destined to be a public speaker she would have been more a little performer from birth, or perhaps it will come later. She will hide under the table if strangers walk into our house. My brother in law said it is because she's been shielded at home for the first 15 months. You know what, crap. I took her out at the end of last year and she is now home permanently.
And you know what, the last time a stranger came to our house it took 3 minutes before she came out and today she told her dad to give her space because she wanted to give the bananas to the guy in the store to weigh it and he had to stand to the side. And she has started greeting strangers. And it had nothing to do with daycare. She saw us doing it, over and over again and nothing happened, so she gained the confidence she needed in her own time.
I'd say give it time. If they push it you might have to put your foot down. Pushing it could have a life long impact on them now. I have a friend with a nearly 4 year old and when you described your son I saw her son. He is exactly the same and I told her she needed to keep her eye on him, he needs her more now than she realises.