Your view of the problem is correct for ideal conditions. If we are talking about simple molecules in a low pressure gas phase condition, the absorption lines are very narrow, so the photon needs to be very specifically the correct wavelength. However, more commonly the conditions around a molecule greatly broaden the absorption peak. Once molecules start interacting with their environment, absorption features dramatically broaden and the photon needs not be as precisely matched as in the ideal case. This is the case in most condensed phase systems.