May I ask you the connection between both segments of your post in bold?
moderate V1-Vr split
consideration is the time taken to accelerate OEI from V1 to Vr which might be quite some knots difference.
but likely to depart the side of the runway with an out of control aircraft
... and all the while you are veering off the runway if you do not have adequate control over the deviation.
In some cases the problem can be addressed by having a high V1/Vr ratio so that the aircraft is off the ground by the time it gets to the Vmcg deviation limit. Some of the older UK certifications were approached in this manner.
Am I correct understanding such statement as
you are probably trying to simplify and generalise too much in your statement. Keep in mind that usually there is some extra control margin due to CG and runway surface providing a lower real world Vmcg than that specified under the certification conditions. The real point in question is that, with a strong crosswind, you MIGHT be in the situation of being below the real world Vmcg on the day. One needs to consider a range of factors to make an assessment. The consequent consideration is to look at how the pilot intends to manage the potential problem (if he chooses not just to ignore it).