One of the titration errors is called "indicator error". It takes a small, but measurable amount, of titrant to shift the color of the indicator. The general rule is to use the minimum amount of indicator needed to get a clear end point.
Generally, the amount of titrant needed is very small. You can adjust for this by running a blank (same reagents as normal, just no sample) and adjusting the titration volume based on the blank.
Had a weird thought. Your original method used EDTA titrations. These methods need to be done in an alkaline environment (say pH 10 for aqueous solutions). Had a similar problem to yours with EDTA. When using a relatively large amount of sample (a calcium salt, in this case), the calcium salt shifted the solution to the acid side. The titration values got funny. Adding a small amount of base before the titration solved the problem.