Distributed scheduling is an attractive approach for the Multiple-Access Channel (MAC). However, when a subset of the users access the channel simultaneously, distributed rate coordination is necessary, and is a major challenge, since the channel capacity of each user highly depends on the channels of other active users. That is, given a detection technique, e.g., Zero-Forcing (ZF), the rate at which a user can transmit depends on the channels other transmitting users have, a knowledge which is usually unavailable in distributed schemes. Fixing a rate and accepting some outage probability when this rate is too high is common practice in these cases. In this paper, we analyze the outage probability of a distributed, asymptotically optimal threshold-based scheduling algorithm under ZF. We rigorously evaluate the distribution of the relevant projections, and give upper and lower bounds on the outage probability as a function of the algorithm parameters.