Can someone really be assigned to review in the APS’s editorial system for over a month without reacting at all and if yes, why?
Yes it really works like this, except that:
(a) the editor selects 1-2 reviewers, not a single reviewer (see http://journals.aps.org/authors/web-submission-guidelines-physical-review). In my experience / field, it's usually two.
(b) I'm not sure which APS journal you are submitting to, but for Physical Review B, the median time with referees is be about 30 days (Rapid Communications) or 40-50 days (regular) in 2013--see https://journals.aps.org/prb/rapids. This is roughly consistent with my experience.
Some journals are much faster.  In my experience in refereeing manuscripts, I'm usually given only 1-2 weeks to respond with "Yes I will review" / "No I will not review".  However, I'm usually allowed to request for an extension of the deadline (and there's usually a box where I'll need to give a justification for the extension).


A 1+ month wait may be a little bit longer than normal--you may wish to consider writing directly to the editor (and if the editor feels there is a need to do so, the editor may choose send an reminder email to the referee). Note that the referee could already be receiving reminder emails (auto-generated by the system)--I have received such emails as the deadline for review approaches.