Does the warped space around the Earth push objects towards the Earth? In the following video, the theoretical physicist Michio Kaku states that space is pushing objects towards the earth. https://youtu.be/fEZupmpTcOU?t=1m59s
Is the warped space around the earth providing a force that is accelerating objects to the earth?
Is this the correct interpretation of Einstein’s mathematical model of gravity?
EDIT:
I do not understand the mathematics of general relativity, but I do have a basic understanding of how the model of general relativity works.

In Newton's theory, gravity makes particles leave their straight paths. In Einstein's theory of general relativity, gravity is a distortion of space-time. Particles still follow the straightest possible paths in that space-time. But because space-time is now distorted, even on those straightest paths, particles accelerate as if they were under the influence of what Newton called the gravitational force.

This quote is from the website einstein-online.
Michio Kaku actually said that space is pushing objects towards the Earth. Did he misspoke?
Frank Wilczek said, “We can describe general relativity using either of two mathematically equivalent ideas: curved space-time, or metric field.”
Kip Thorne said, “You can reformulate Einstein’s laws in a sort of Newtonian way” https://youtu.be/rHsBDTy3yEE?t=5m7s
I am wondering if there is more than one valid interpretation of what Einstein’s mathematical model of gravity actually represents.
 A: No, warped space is not "providing a force". Gravitation warps the space. In other words, the causality is gravitation->warped space, so you/Kaku have it backwards. Notice that, as with other causal effects, the warping of space travels at the speed of light.
A: Actually, it's not the warping of space, it's the warping of time, and yes it is (on a cause -> effect basis*) warped time -> gravity... *though cause/effect is not necessarily a true way of understanding it... 
using a very simplified explanation
F=ma... a=ds/dt, where s={x,y,z}... dt=(tb-ta)
F is proportional to ds and 1/dt... space doesn't actually curve (warp) that much, at least not enough to have any evidence or effect on the force of gravity. 
so if ds isn't changing, then we're left with Fg proportional to 1/dt... as time slows approaching mass, dt gets smaller, as the length between ta and tb gets longer... therefore, the acceleration increases the closer 2 masses are together. more acceleration represents more force. as GR defines gravity as a result of acceleration toward the center of mass, the warping of time, therefore, causes the change in acceleration which changes the strength of the force... 
I know this is a very simplified explanation without getting into Einstein's equations, they can be reduced essentially to a F=ma form and are related proportionately. 
