Every dentists in the US has to have a DMD or DDS degree to be licensed to practice or go through an advanced standing program. You can't open a dental office with a dental degree from Mexico, Australia, etc.
Bottom line.. it not a problem and really a non-issue!
It has nothing to do with whether your degree is titled DDS, DMD, BDS, BDent, BDSc, BChD, etc. It has to do with accreditaiton.
Example.. all Japanese dental schools grant DDS, but their dental schools are not accredited in the USA or Canada. However, Many dental schools in Australia grant a BDent, BDS, BDSc, DMD, DDS, and they are all accredited in Canada (and may be accredited in USA at some point should the US decide to join the agreement).
Also, every state in the US has a separate dental board (e.g: separate licensure requirements). For example: Minnesota will allow those with foreign dental degrees (again doesn't matter if its a DDS, DMD, BDS, LDS, BChD, BDent, etc) to sit the state dental licensure exam without doing any further training!! ... and some states only require a CODA accredited dental residency ... and yet some states require you graduate with a CODA accredited undergraduate dental degree. So you can't generalize about licensure requirements in the states.
On the other hand.. Dental licensure in Australia is Nation-wide now and not state based. So there are no loopholes to getting an Australian license by going through a separate state with different standards!