Phylogenetic trees are routinely visualized to present and interpret the evolutionary relationships of the species that are being studied. Virtually all empirical evolutionary data studies contain a visualization of the inferred tree with support values using one of the popular and highly cited (e.g., TreeView, Dendroscope, FigTree, Archaeopteryx, etc.) tree viewing tools. As a consequence, programming errors or ambiguous semantics in tree file formats can lead to erroneous tree visualizations and consequently incorrect interpretations of phylogenetic analyses. Here, we discuss the problems that can and do arise when displaying branch support values on trees. Presumably for historical reasons, branch support values (e.g., bootstrap support or Bayesian posterior probabilities) are typically stored as node labels in the widely-used Newick tree format. However, support values are attributes of branches (bipartitions) in unrooted phylogenetic trees. Therefore, storing support values as node labels can potentially lead to incorrect support-value-to-bipartition mappings when re-rooting trees in tree viewers. This depends on the mostly implicit semantics of tree viewers for interpreting node labels. To assess the potential impact of these ambiguous and predominantly implicit semantics of support values, we analyzed 10 distinct tree viewers. We find that, most of them exhibit some sort of incorrect or unexpected behavior when re-rooting trees with support values. We find that Dendroscope interprets Newick node labels as simply that, node labels in Newick trees. However, if they are meant to represent branch support values, the support value to branch mapping is incorrect when re-rooting trees with Dendroscope. We illustrate such an incorrect mapping by example of an empirical phylogenetic study. As a solution, we suggest that (i) branch support values should exclusively be stored as meta-data associated to branches (and not nodes), and (ii) if this is not feasible, tree viewers should include a user dialogue that explicitly forces users to define if node labels shall be interpreted as node or branch labels, prior to tree visualization.