@Recc
Unless she has a very long anchor rode then she is certainly underway. There is no AIS navigation status code for 'stopped', so presumably that is the website filling in the details from the SOG rather than a real status change. I wouldn't read too much into it.
It is doing under 0.1kn its basically stopped, it most likely has engines shut off and is slowly moving with the current.
I have seen the status stopped numerous times on various vessels when they are basically engines off but not anchored and a lot of fishing vessels show this.
For example,
http://www.marinetraffic.com/ais/ind.../direction:asc this is history for a NZ fishing vessel.