More than two years after its outbreak, the COVID-19 pandemic continues to plague medical systems around the world, putting a strain on scarce resources, and claiming human lives. From the very beginning, various AI-based COVID-19 detection and monitoring tools have been pursued in an attempt to stem the tide of infections through timely diagnosis. In particular, computer audition has been suggested as a non-invasive, cost-efficient, and eco-friendly alternative for detecting COVID-19 infections through vocal sounds. However, like all AI methods, also computer audition is heavily dependent on the quantity and quality of available data, and large-scale COVID-19 sound datasets are difficult to acquire -- amongst other reasons -- due to the sensitive nature of such data. To that end, we introduce the COVYT dataset -- a novel COVID-19 dataset collected from public sources containing more than 8 hours of speech from 65 speakers. As compared to other existing COVID-19 sound datasets, the unique feature of the COVYT dataset is that it comprises both COVID-19 positive and negative samples from all 65 speakers. We analyse the acoustic manifestation of COVID-19 on the basis of these perfectly speaker characteristic balanced `in-the-wild' data using interpretable audio descriptors, and investigate several classification scenarios that shed light into proper partitioning strategies for a fair speech-based COVID-19 detection.