Because as soon as you get rid of the overlaps, the integration of the equations of motion becomes numerically stable. And a stable integration reproduces the correct physics of particle collision, as you described it. By pure thermal fluctuations, the particles never come closer than 0.9*sigma (you use the standard LJ potential). More precisely, the probability that this happens during the simlation is negligible.
inter ljforcecap 0 switches off the capping and uses the full potential (please read the manual).
With best regards,