This statement is not true, except regarding recoil.
The 300 WM and 7mm Mag have, for all intents and purposes, identical flight ballistics. The 7mm does not shoot significantly "flatter" than 300 WM. With bullets of similar sectional density and B.C., the two rifles achieve nearly identical velocities. Individual rifles and loads may vary, but on the whole, the two are effectively the same for drop/wind when comparing apples to apples.
For example:
7mm 180 Berger Hyb Target = 0.680 BC, ~2900 fps in 24" barrel
300 WM 215 Berger Hybrid Target = 0.691 BC, ~2875 fps in 24" barrel
IMO, neither caliber is appropriate to use on elk at 1000 yds, unless you are an outstanding shooter, in perfect conditions. Even then, it's literally "marginal" by nearly all bullet manufacturers standards (i.e >1800 fps impact)
For example, at 1000 yds, using a best case scenario with high BC target bullets, specifically NOT recommended by the manufacturer for hunting:
7mm 180 Berg Hyb Targ @ 2900 fps = ~1850 fps, 1300 ftlbs
300 WM 215 Berg Hyb Targ @ 2875 fps = ~1850 fps, ~1650 ftlbs
300 WM will give you ~15% more "killing power" at any given distance over 7mm Mag. This is just a matter of physics. Roughly 15%-20% bigger hole, 15%-20% more momentum, 15%-20% more energy, and of course roughly 15%-20% more recoil.
In my experience shooting silhouette the 7mm ballistics are better than the 308, reason why the 7mm-08 replaced the 308 Win in this competition. The 7mm bullet shoots flatter than the 308, just like the 6.5 shoots flatter then the other two, this is what I've experienced.
As far as the capabilities of the 7 RM and the 300 WM, in the hands of a trained shooter and hunter they are definitely capable of proper killing at a 1,000 yds, under the right conditions of course.
Maybe the shooter is not capable but a properly set up rifle is with the correct bullet is. The barrel length should not be 24", a 28" or 30" is best so you can push the bullet faster.