I'm sympathetic, but don't make the discussion worse by throwing falsehoods like this around.
Besides the fact expressed by others that physically illness is more diagnosable, you typically don't get mentally ill from being in proximity to a mentally ill person. (At least, I never have.)
Physical illness is a different situation. That's why my workplace offers near unlimited sick time for this reason. As much as we'd love you have to working, we don't want your diseases.
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(Granted, having an anxiety attack in the middle of work may not do wonders for the mental state of your coworkers, but blithey asserting this "no different" is dubious at best.)