In 咱們祖國的香港:
all visa /immigration related rules have one exception, i.e. the general rules do not apply to mainland chinese who are living in mainland. However, Oversea chinese (i.e. chinese who have been living in other countries over 2+ years) are not in this category.
Your probably can consider the following options:
(a) get your daughter back to US/where you are, and apply to HK government for the entry permit.
or
(b) get her a visitor visa to HK from the china city where she is now, you can go to a travel agency for such arrangement, or go through your friend-network to find someone in charge of issuing such permit (e.g. police dept?) to get her a visitor visa to HK. Once she is in HK, she can apply for the proper visa for her summer intern, with her oversea chinese status. I assume it should be working-permit/visa. With a tourist visa, she can start to work in the company, but the company cannot and should not pay her, because it'll be illegal. But the company can backdated pay her after she gets her working-permit.
One way another, you should check with the HK immigration dept. Check with chinese embassy (in US or where ever) is useless if it's regarding HK residency issue.
good luck.
M2C ;-)