300 customers on a recency × frequency plane (scaled). There are no labels — only structure. Choose k, drop the centroids, and step the algorithm: assign every customer to the nearest centroid, move each centroid to the mean of its members, repeat. Then check the elbow and silhouette — and notice k-means will confidently find clusters whether or not they exist.
What k-means assumes: clusters are compact, roughly spherical, and similar in size, and distance means the same thing in every direction — which is why you scale (and log) RFM features first. What it never tells you: whether clusters exist at all, or how many the business can act on. The elbow and silhouette inform k; the marketing calendar decides it.