Yeah, I have since become quite suspicious about that site. I have been told by a more reputable source that it is the ions that have the beneficial effect.
However, an ion is not an atom :-) What they are saying on invive is that in their product, there are more silver particles that do not have a net charge (typically, silver atoms are stripped of an electron (or is an electron added? I forget) to make an ion in solution. This is what the electrolysis produces.