Independent-Root Counts Do Not Characterize Local Graph Removal

We give counterexamples to the fixed-cardinality independent-root criterion for local graph removal in Conjecture 8 of the 2026 Oberwolfach report Combinatorics. For any core graph with a maximal independent set smaller than its independence number, retaining that set as singleton parts and blowing up the other vertices gives graphs a positive normalized maximum-degree distance from being H-free, while every independent root count of the prescribed size is asymptotically small. A six-vertex wheel is an explicit example. For C9, the construction has 6m+3 vertices, maximum independent-four-root count m^4, and exact local removal distance ceil(m/2)/(6m+3), tending to 1/12. No single root cardinality can characterize local removal for such cores. The result concerns the literal printed criterion, including independence in the copy; it does not exclude formulations testing several root sizes or resolve the broader frozen UnsolvedMath OWR-14299905-027 question about all possible variants. The unpublished intended graph-removal manuscript was not obtained, so no claim about a corrected intended theorem is made. This five-page unrefereed preprint was developed with AI assistance and self-audited. Integer regression checks, independent small cycle enumeration and finite SAT deletion checks supplement the complete written proof; they are not independent referee review or formal proof-assistant verification.