Trust has been shown to be a key factor in effective human-robot collaboration. In the context of assistive robotics, the effect of trust factors on human experience is further pronounced. Personalization of assistive robots is an orthogonal factor positively correlated with robot adoption and user perceptions. In this work, we investigate the relationship between these factors through a within-subjects study (N=17). We provide different levels of customization possibilities over baseline autonomous robot behavior and investigate its impact on trust. Our findings indicate that increased levels of customization was associated with higher trust and comfort perceptions. The assistive robot design process can benefit significantly from our insights for designing trustworthy and customized robots.