It's not that strange a point, it's like trying to suggest a humble desktop calculator can compute all the decimal places of pi. The calculator is obviously finite in build and it's actual built to round off to a certain decimal place because of it's finite design (The screen has a fixed amount of numbers it can display). However beyond that rounding there is still infinite numbers to be read in ever greater detail.
Now you could use the calculators output in a mathematical sum but it's accuracy is far depleted in comparison to more accurate outputs which consist of further iterations of decimal place.
In fact comparing the two sum's you will find the disparity grows with each iteration of decimal place. It's somewhat similar to a 'Butterfly Effect', in fact very close to an example that you'll find in the book 'Chaos' by James Gleick. I believe the reference is in regard to research done into predicting weather patterns and how such predictions were greatly altered by the depths of the decimal placing. (Rounding is a no-no in regards to precision.)
What I am suggesting is yes our planets output gravity at a higher level based upon our proximity, however this doesn't mean that we aren't effected by gravity from other planets in other solar systems the effect however is of course very, very, very minimal.