I think you have a genuine reason for concern here. There are plenty of stories of gifted children running off to school excited to learn something, finding little of that, and reacting in negative ways, often times with lifelong consequences. You have an educator telling you that your child fits this profile.
The first thing I would do is read that acceleration and early entrance policy in close detail.
The next thing I would do is explore your sister's comments more thoroughly, because WHY she feels the way she does may be important. How alike is your child to hers? How do her concerns match up to your DS?
And then I would go ahead and ask for that early entrance referral from your DS' teacher, and use that as a starting point for conversations with prospective schools.
I would not approach the schools with the question "Can you test my DS for giftedness?", because:
1) Cognitive test results at that age are quite unstable.
2) It comes off as tiger-mommish.
Rather, by talking to them about early entrance, and when they ask why you're interested, you share the statements of your DS' teacher and the referral she has provided, you're on stable ground, and your concerns are coming from someone else besides you.
These conversations don't commit you to early entrance, but it could be very educational to see what sort of institutional support or opposition you're facing.
