In the study of WANG et al, they discovered "the different effects of different low-molecular-weight heparins on the activated clotting time may be related to the different anti-IIa activities." Thus, taking 2 different brands may have adverse interaction. (
In vitro anticoagulation monitoring of low-molecular-weight heparin)
One possible answer too is that different brands correspond to the 3 different LMWH types. Doses and indications differ between three medicines, thus these drugs can not be used interchangeably for one another. Also, clinical trials on comparison of the different LMWH types and the possibility to be used in place of the other are still scarce.
Another article which supports the statement you quoted is:
Low molecular weight heparin for venous thromboembolic disease