How by the fact that mass ratios are identical can we conclude that mass is independent of the source of acceleration? I am currently studying Kleppner D., Kolenkow R. - An Introduction to Mechanics, and I stuck at a point where they show that by carrying further rubberband experiment, 

By causing motion using springs and magnets or any other source, we found that ratio of acceleration, hence the mass ratio are identical no matter how we produce acceleration, provided that we do the same thing to each body

This till here was understood.
but then they continue to conclude that

Thus, mass turns out to be independent of the source of acceleration, but appears to be inherent property of the body.

I can not understand how mass ratio being constant implies that mass does not depends on source of acceleration (or force as I understand it). As ratio of acceleration is also identical but it depends on the force.

 A: I believe the author is saying that if two objects exhibit different accelerations when subjected to the same force, there must be some property that is determining how much that object should accelerate.
As it turns out, as the force is increased, ("no matter how we produce acceleration"), the same accelerations increase in the same ratio.
I.e. if we double the force, both objects' accelerations double, but the ratio between their accelerations, such as one being three times larger than the other, stays the same.
This is why the author concludes that this property, called "mass", must be an "inherent property of the body", and be independent of the conditions applied to the body (unlike, say, colour which changes with different lighting conditions).
For example: say we apply a force of $1$N to two bodies, and see that they accelerate at $2\text{ms}^{-2}$ and $6\text{ms}^{-2}$. Then the author is saying that if we were to increase this force to, say, $2$N, then, although their accelerations would increase (here to $4\text{ms}^{-2}$ and $12\text{ms}^{-2}$), the ratio of their accelerations stays the same: $1:3$.
So there must be something inherent that tells the objects how much to accelerate - this is mass.
A: If you have a standard for measuring force (such as a spring scale), then the force from any source (gravity, electrostatics, magnetism,etc.) can be calibrated in terms of that standard.  (Hence the constants in force equations.)  So a given force, from any source, acting on a given mass, will produce the same acceleration.
