An Annual Inspection is just that an Inspection!
You can (if the mechanic/IA allows you to) help with the Annual Inspection (Owner Assisted Annual Inspection). We encourage you to get involved with this process, you will know your aircraft better and it will help you get and keep a handle on the cost of your Annual Inspection.
Routine servicing is NOT a part of the annual inspection. The inspection itself is essentially a visual evaluation of the condition of the aircraft and its components and certain operational checks. The person performing the inspection may recommend certain services to be performed at various operating intervals. These services can often—in fact, should—be done conveniently during an annual inspection, but are not considered to be a part of the inspection itself.
In other words, you DO NOT have to have your aircraft serviced during an Annual Inspection. It is often easier and more convenient for servicing to be done during an Annual Inspection, and you can do some of this work your self, before the inspection. (it’s a good idea to work with your mechanic/IA on this so there is no duplication of servicing and so he/she are OK with you doing the work. (we will get into the items you can do yourself later.)
FAA regulation state that:
The procedures and scope for annual inspections are set forth in 14 CFR part 43, appendix D, and should be followed in detail. The scope and detail of 100-hour and annual inspections are the same.