So, do you agree that as long as density of any inner shell (when the object is just at EH) of radius r is < 5.3*10^25/r^2, all the inner points shall be out of their respective EHs?

The task is to find an object that has an event horizon internally, but we have to avoid hitting this condition for any radius: d(r) > 5.3*10^25/r^2

Imagine an object with a radius larger than 1 meter. We're going to focus on the core up to 1 meter, and we're going to check whether there's an event horizon there. In other words, we are going to check whether $$r_s$$ is larger than 1 meter at an $$r$$ of 1 meter.

Let's calculate the mass of this core, by assuming it's right on the edge; in other words, all throughout the core the condition is met exactly. Now, writing out the maths is boring and silly-error prone, so we're going to be lazy and use one of Wolfram Alpha's widgets, the Spherical Integral Calculator:

http://www.wolframalpha.com/widgets/view.jsp?id=89c969c21b169fa996f899d9b2a98588
Let's put in the density condition: (5.3*10^25)/(rho^2) (in mathematics, they often use rho instead of r)

And integrate rho from 0.000001 to 1, phi from 0 to 2pi, and theta from 0 to pi (just look at:

https://en.wikipedia.org/wiki/Spher..._and_differentiation_in_spherical_coordinates under "Thus, for example, a function...").

Result: 1.05*10^33 (kg)

This is the mass of the core; in other words, this is the maximum possible mass of an object of 1 meter that can still meet the condition.

To check whether this object has an event horizon, we calculate its Schwarzschild radius:

$$r_s=\frac{2GM}{c^2}$$

This gives:

$$r_s=1.485*10^-27\times1.05*10^33=1.6*10^6$$ (in meters)

Since $$1.6*10^6>1$$, we have $$r_s>r$$, and thus there's an event horizon around this object.

Note that we're missing the mass up to 0.000001 meter, because there's an infinity hiding there, so there's even more room for adding mass to this object.

Conclusion: something must have gone wrong in the derivation of the density condition, because there are objects possible that meet the condition while violating what it should stand for.

In other words: obviously I do not agree, no.