What you've assumed is true stickN'rudder007, Vmu (which is expressed as a CAS) should remain unchanged, but............
If you read further into your notes, the author may well be referring to TAS at Vmu, which WILL decrease with increased Air Density. The TAS is directly related to the Ground Speed, which is directly related to the runway distance used, thus, from a Runway Performance aspect, the Ground Speed at Vmu will reduce with increasing density, which is significant.
Now here's a nit-picking one, Vmu is actually related to EAS, not CAS, but at typical Takeoff speeds and altitudes there's only a slight difference. Nevertheless, for a given EAS, CAS will decrease with increasing Density. Consider for example an aircraft with a Vmu of 130 KEAS for a given weight and configuration at ISA Temperatures -
At Sea Level : Vmu = 130 KEAS = 130.0 CAS
At 5,000 ft : Vmu = 130 KEAS = 130.1 CAS
So at the higher density Sea Level Airport, Vmu is 0.1 Kt CAS lower, nit-picking indeed!
Regards,
Old Smokey