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I'm reading DNA Topology: Fundamentals from where I quote :

Topological aspects of DNA structure arise primarily from the fact that the two DNA strands are repeatedly intertwined. Untangling these two strands, which occurs in all major genetic processes may prove rather difficult. In the simplest case of a linear DNA in solution, untangling is possible due to the free rotation of the ends of the DNA. However, for all natural DNAs, free end rotation is either restricted or forbidden altogether. Consequently, untangling the two DNA strands becomes topologically impossible.

And from Wikipedia:

However, a circular chromosome can provide other challenges for cells. After replication, the two progeny circular chromosomes can sometimes remain interlinked or tangled, and they must be resolved so that each cell inherits one complete copy of the chromosome during cell division.

enter image description here

Is there any evidence that proves the idea represented in the figure?

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Yes, there is an abundance of evidence. I think the following electron micrograph is pretty convincing.

enter image description here

This image is from a review:

Gil-Ramirez G, Leigh DA, Stephens AJ. 2015. Catenanes: Fifty Years of Molecular Links. Angew Chem Int Ed 54:6110-6150.

It was adapted from the first paper to observe naturally occurring catenated DNA molecules, which were isolated from HeLa mitochondria:

Hudson B, Vinograd J. 1967. Catenated Circular DNA Molecules in HeLa Cell Mitochondria. Nature 216:647-652.

You can see this answer for an explanation of why catenanes form during replication:

How do catenanes form when DNA replicates?

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