People driving into battle in a G-wagon are courting trouble to begin with, but that isn't exactly what we are talking about.
A Mech unit, regardless of its name, has certain attributes based on the use of weapons platforms and transport. A mech unit is fast, hard hitting and protected. A mech unit also needs a large and flexible logistics tail, and is vulnerable to close in threats (IEDs, mines, ambush, etc.) The dismounted soldiers in a mechanized unit use their infantry skills differently than a Light Infantry unit would. Patrolling would be close in to clear the area around a combat team hide, for example, while the defense involves using the dismounted troops to provide close in protection for the major weapons platforms (who gets sited first; the rifle trench or the tank?). Additional skills are needed to direct the fire of major weapons systems (i.e. shooting a target using a tank telephone), and in offensive operations, the dismounted soldiers would work in close cooperation with the heavy weapons platforms. Because of the size and volume of the turret and ammunition, Mechanized Infantry tend to have much smaller sections by default. As a partial way of making up for this, Mechanized soldiers rely on heavy weapons which require vehicles to use effectively (25mm, .50 HMG, 40mm AGL, 81mm mortar, TOW, etc.) While many of these weapons could be "man packed" in theory; the amount of time and effort needed, and the minimal amount of ammunition that could be carried makes this a rather impractical idea.
The Light Infantry would work at long range, so to speak, conducting dismounted recce or fighting patrols well away from their patrol base, setting defenses without the use of tanks or heavy weapons, and (borrowing from the "Towards a true Light Infantry" thread) engaging the enemy through "sniping" attacks rather than attempting to use shock assaults. Enemies who require shock assault tactics can be "pinned down" by the LI until a more robust force arrives (it was claimed a single sniper could hold up an entire battalion in WW II), or until the LI could vector in fast air/artillery or helicopter firepower on the target.
It is certainly true that well trained soldiers can and will be able to move from mounted "Dragoons" to stealthy "Light Infantry", but as I hope my examples have shown, this isn't a simple matter of climbing aboard or dismounting from a vehicle. Since there are not enough vehicles to constantly train in mechanized tactics, and our vehicles are at the low end of the scale compared to "Warriors" or M-2s, Canadian soldiers are a more hybrid force than most, so the transition between roles is quite a bit easier than in a more richly equipped force.