Without knowing the source of your information, it is difficult to know just where the author is coming from. Possibly the text meant to say Vmca rather than Vmcg and is just a typo. Alternatively, Vmcg-limited V1 could lead to a similar incidental effect on V2 at low weights.
However, it is useful to review the generic story from time to time as there are some traps here for young players which can bite hard and Mutt and I like to run it past the new people in the forum every now and again.
If I may talk twins, which is what I normally play with (only the factors change .. not the basic story).......
V2 normally is scheduled as the minimum permissible V2 to keep the takeoff distances down.
The certification rules require, for the configuration, that minV2 (or V2min - take your pick) be not less than
(a) 1.2 x Vs for the weight
(b) 1.1 x Vmca
Typically, for any aircraft,
(a) at lower weights, the Vmca requirement will become limiting. By this one means that 1.1Vmca is greater than 1.2Vs. In this region, V2 doesn't vary with weight.
If Vmca is very low, this effect may not be seen .. the Citation, if I recall correctly, is an example. However, I would be very surprised if a wing-mounted four-motored bird did not exhibit the effect.
(b) as the weight increases Vs increases and, at some point, 1.2Vs increases above 1.1Vmca ..... now V2 increases as weight increases.
To check this out, have a look at your standard speed schedule with weight. At low weights, V2 is constant and doesn't vary with weight .. you are Vmca-limited. As the weight increases, you get to a point where V2 starts to increase as weight increases.... you are stall-limited.
A consideration which often is overlooked in training is that the handling problems with a failure, say, halfway through the rotation flare are VERY critical if V2 is Vmca-limited and, depending on Type yaw-roll coupling characteristics, you might need a lapful of wheel rotation to control bank ... Vmca is very bank-dependent ... if you don't control bank, Vmca increases rapidly due to slip ... and you SUDDENLY find yourself in the middle of a Vmca departure ... crash, burn, die. Well worth investigating this in the sim ... just a confidence and co-ordination training exercise ... but to experience it in the aircraft for the first time is not a good thing. Those who haven't played with it might be non-believers ... those who have will smile knowingly ....
As we back up a little on the takeoff, VR is relevant. In essence, VR is a convenient speed chosen so that the OEI rotation will result in somewhere near V2 at screen height. VR will sit somewhere between V1 and V2.
Backing up further, we have to concern ourselves with V1. V1 is limited on the high side by VR and on the low side by Vmcg.
If Vmg is sufficiently high, then minV1 may be high enough at low weights to require that VR be increased which, in turn, might require that V2 be increased. (This may be what the original text was referring to).
If the aircraft is typical ..., in the same way that the speed schedule shows a constant Vmca-limited V2 at low weights, there will be a constant Vmcg-limited V1 at low weights. So, even if Vmca were not going to be a problem, in the scenario described in the previous paragraph, we could see the Vmcg-limited V1 imposing an incidental non-weight-related limitation on V2 at low weights.
As with Vmca-limited V2, there is a trap associated with Vmcg-limited V1 takeoffs.
For the US case, certification Vmcg is determined for NIL WIND. However real world actual Vmcg is highly crosswind dependent. Typically, the effect of crosswind might be to increase the real world Vmcg by half the crosswind for a twin, to more than the entire crosswind for a four-motored bird. So, if you are scheduling a Vmcg-limited V1 takeoff in a strong crosswind ... then you may be between a rock and a hard place.
If the speeds are limited severely by runway distances, then I guess you are stuck with it .. either you go and risk losing the aircraft with a critical failure (and, again, if you have a good sim model, the sim exercise is useful training to hammer this point home), or you delay until the wind abates.
If you are just doing a ferry flight, say, and you have a long runway, do consider increasing the speed schedules in accordance with the OM tables, to a point where the actual V1 is increased sufficiently above Vmcg-limited V1 to take account of the real world increase in Vmcg due to the actual crosswind. So long as you stick with a published speed schedule appropriate to a weight not greater than the RTOW for the runway, then you shouldn't have a problem. Certainly, if you are scheduling a Vmcg-limited V1 with an aft CG, in a strong crosswind, and you lose the upwind engine at or near to V1, then you WILL be in for an interesting ride, especially if there is much in the way of a V1 to VR split scheduled for the takeoff.
One should keep in mind that real world (as opposed to certification) Vmcg and Vmca are very CG dependent.