Could an exposure to a small amount of viruses result in an easier course of the disease?
I think the answer to your question is actually found in the paragraph surrounding the quoted statement:


  Auch Gunther Hartmann, Professor für Klinische Chemie und Pharmakologie an der Universität Bonn, berichtete, nach ersten vorsichtigen Einschätzungen sei davon auszugehen, dass der Schweregrad der Erkrankung über Hygienemaßnahmen reduziert werden könnte. "Die Zahl der Erreger hat bei Erstinfektionen Einfluss auf den Schweregrad der Erkrankung."


Approximate translation:


  Gunther Hartmann, Professor of Clinical Chemistry and Pharmacology at the University of Bonn, also reported that, after initial careful assessments, it could be assumed that the severity of the disease could be reduced via hygiene measures. "The number of pathogens influences the severity of the disease in initial infections."


Notice that the language is not absolute but rather asumptive: "initial careful assessments," "It could be assumed," "could be reduced."  It's tentative language and suggests that research is ongoing.  Furthermore, if you search for that quote, you'll find that this is not published in peer-reviewed journals; it's simply a preliminary observation to encourage the public to limit intake of pathogens.

We already know that in some other cases the viral load affects the severity of symptoms. But we don't actually know that that's the case with COVID-19.  In fact, initial reports from Italy suggest that there is no statistical difference between viral loads between symptomatic and assymptomatic cases of COVID-19. So Chris's short answer is absolutely right; we don't know.  For all practical purposes, it's just as well to assume that it's the case, as it will lead to more hygeinic practices, but further research will be required to demonstrate that it is actually the case.