This paper explores the application of molecular communication via diffusion-based nano-sensor networks (MCSNs) for data gathering applications in in-body medical systems. For MCSNs, the large and varying propagation delay in the channel presents a fundamental challenge for channel access, leading to packet collisions. Although packet collisions are well-studied for traditional wireless sensor networks, to date, there are no such studies conducted for MCSNs. Another fundamental challenge is the limited capabilities of the nano-sensors, rendering the existing solutions inefficient. Therefore, a novel light-weight time-division multiple access (TDMA)-based data gathering multiple access control (MAC) protocol is proposed. Light-weight here implies that long information, such as timestamps, is not exchanged. TDMA-based here implies that each nano-sensor is designated an exclusive time-slot. The lack of a channel model for spherical transmitters impairs theoretical analysis of the probability of packet collisions. To overcome this, the propagation delay is approximated as a Normal distribution. The model is validated using the widely popular particle-based simulation, which is also used to determine the packet duration considering ON-OFF shift keying. Building upon these analyses, a system-level simulator is developed to evaluate the proposed MAC protocol. For the first time, the packet collision probability is characterized under varied distances and diffusion coefficients. A key finding is the correlation between the channel utilization and the time-slot occupancy ratio, which can be used as a tool to optimize the performance of an MCSN. Finally, comparisons with conventional TDMA reveals that the proposed protocol can offer better performance.