The site's wording fails at the smallest subgraph sizes. Its hypothesis quantifies over every subgraph on $k$ vertices, including $k=1$, and a single vertex has $0>2\cdot1-3=-1$ edges, so no graph with a vertex satisfies it (the vertexless graph, if admitted, fails at $k=0$, where $0>-3$); the question then concerns an empty class of graphs and holds only for want of an instance. The failure is this page's own elementary check. The defect is already in the posers' text: [EFRS93] Question 1 (p. 398) asks "If every subgraph $S$ of $G$ satisfies $q(S)\le2p(S)-3$, is $G$ necessarily Ramsey size linear?", and its prose form on p. 395 ("each subgraph $H$ of order $m$ has size at most $2m-3$") is unrestricted as well. The change inserts "$\geq 2$" after "any subgraph on $k$", which excludes exactly the sizes $k\le1$ at which no graph can meet the hypothesis; it is an exclusion of size-degenerate values, the formal-conjectures file states the same restriction to vertex sets of at least two elements (it follows the site and is not a further source), and no source of higher rank supplies a range. Above the excluded sizes no failure remains: for $k=2$ and $k=3$ the bound ($1$ and $3$ edges) holds in every graph, and at $k=4$ it excludes exactly $K_4$, which is not Ramsey size linear by [EFRS93] Corollary 1 ($p=4$, $q=6=2p-2$). No result about the site's wording exists beyond the vacuity check recorded here, which settles no instance of the corrected Statement.