A desktop layout can technically fit on a phone and still work badly. Long lines, small buttons, tables, and heavy images require content and technical decisions. We therefore check widths between phone, tablet, and desktop sizes, too. A page can look fine at both extremes while a menu overlaps a button at an intermediate width that those screenshots never show.
We test important pages visually and measure whether components extend beyond the viewport. We check images and complete the agreed tasks on real devices or realistic emulators. Longer copy and zoomed views are part of those checks. This reveals specific faults; a single homepage screenshot does not prove the whole site works responsively.