Reeb graph of the tilted torus

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Reeb graph :https://en.wikipedia.org/wiki/Reeb_graph

some pictures: http://www.math.brown.edu/~banchoff/Beyond3d/chapter3/section08.html

The Reeb graph of an upright torus, which I'll call "a vertical torus", of the height function has a loop since there exists a horizontal slice resulting in two separate connected components.

The Reeb graph of a toppled over upright torus, which I'll call "a horizontal torus", of the height function doesnt have a loop.

Certainly a slightly tilted vertical torus has Reeb graph with loop by inspection.

Is this true for all angles of tilt leaving only the perfectly horizontal torus without a loop in its Reeb graph?