  We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke
[3] who recently used Lie algebroid gauge theories to obtain sigma models
exhibiting a "T-duality without isometry". We point out that those
T-dualisability criteria are not written invariantly in [3] and depend on the
choice of the algebroid framing. We then show that there always exists an
isometric framing for which the Lie algebroid gauging boils down to standard
Yang-Mills gauging. The "T-duality without isometry" of Chatzistavrakidis,
Deser and Jonke is therefore nothing but traditional isometric non-Abelian
T-duality in disguise.
