UMLR — Vertical lines do not always describe the time-line for an interaction diagram

In an interaction diagram each vertical line describes the time-line for a process, where time increases down the page.

This is only true for sequence diagrams. Timing diagram use horizontal ordering. Communication and Interaction Overview diagrams may have incidental non-time ordered vertical lines.

The following text from the spec should be qualified to only discuss sequence diagrams

17.1.3 Partial ordering constraints on valid and invalid traces
...
In an interaction diagram each vertical line describes the time-line for a process, where time increases down the page.

17.3.3 Semantics
Lifelines
In an interaction diagram a Lifeline describes the time-line for a process, where time increases down the page