"Exactly your level" may not be your level at all. Relative altitudes are notoriously difficult to gauge by eye alone.
An aircraft at your level almost always looks as if it's well above you. Without the benefit of a direct feed from the TCAS, it's impossible to be sure the other aircraft was at your level.
What is most likely the case was a regular turn at a waypoint, or the begiinning of an offset instruction at the precise moment another aircraft passed by, at the opposing level.
TCAS functions from 40nm out - rapid, emergency manoevres are normally rare and generally in the vertical plane.
Good question though, and a keen observation.
TCAS = Traffic Collision Avoidance System