"Should I follow the equipment manufacturer's recommendations on a specific brand of lubricant?"
This is an operational and monetary question as much as it is a mechanical maintenance question.
The fundamental issues are:
1. Is the machine still in warranty?
2. Are you required to use this particular lubricant to maintain warranty?
3. Do the instructions give you sufficient information regarding lubricant specifications so that you can use your own judgment in selecting a suitable alternative?
4. Do you have a product on-hand that has nearly identical fundamental characteristics, such as viscosity, viscosity index, oxidation resistance, wear resistance, demulsibility, corrosion protection, etc.?
5. Will the addition of another lubricant mean greater complexity and greater operational cost for this piece of equipment?
There is generally no magic in a product brand name. There are exceptions, and in those cases, the equipment manufacturer will let you know up front what is necessary for you to maintain warranty.