Copied from the site you linked:
Moped drivers are required to abide by the same traffic laws and regulations as automobile drivers. Detailed information on Virginia's traffic laws and regulations is available in the Driver's Manual. In addition, certain local governments may impose restrictions on moped operation. Violations of the moped laws are considered a traffic infraction and convictions will appear on your driving record.
All DUI laws apply to mopeds operated on public highways.
No moped shall be driven on any highway or public vehicular area faster than 35 miles per hour. If you operate a moped faster than 35 miles per hour, Virginia law deems this to be operating a motorcycle, which requires you to title and register the moped as a motorcycle and obtain a motorcycle license. Operation of mopeds is prohibited on any Interstate Highway System.
I think the area in red is what you may need to focus on in order to get the complete information you are seeking.
The area in Green slightly differs from what you posted but this only helps your arguement even more as it does not say that the vehicle can not be capable of driving faster but only that the vehicle can not be operated at a higher speed.
I am going to keep searching until someone posts up a link to a specific law that clears everything up. or I get tired of looking.