Why can't ligands with "locked structures" undergo chelation? The following quote is from the book Concise Inorganic Chemistry by J.D. Lee (Adapted by Sudarsan Guha), from the chapter "Coordination Compounds", page 177:


  ...it must be noted that $\ce{NH2NH2}$ and $\ce{N(CH2CH2)3N}$ cannot act as chelating ligands due to the formation of a three membered ring and locked structure respectively.


But, as per the accepted answer to the question Are all complexes with a polydentate ligand examples of chelation?, when a ligand forms more than two bonds to the central atom, the result is a chelated complex. This is also inline with the IUPAC Gold Book's definition of Chelation:


  The formation or presence of bonds (or other attractive interactions) between two or more separate binding sites within the same ligand and a single central atom. 


As per my understanding, it doesn't seem to exclude any ligands as mentioned in my textbook.

I can understand that since $\ce{NH2NH2}$ forms a three membered ring, there would be ring strain in the structure and hence the process of chelation is not energetically feasible compared to four membered (or higher) rings. I think this would be the same for all such ligands with donors adjacent to each other, as I have not encountered any such species so far.

However, I'm unable to understand why $\ce{N(CH2CH2)3N}$ (1,4-Diazabicyclo[2.2.2]octane) cannot undergo chelation.



From its molecular structure, I can imagine that the three ethylene groups act as springs to accommodate any ring strain while bonding with the central atom and so there must be no hinderance to undergo chelation. The following molecular structure is what I think might be if $\ce{N(CH2CH2)3N}$ undergoes chelation with cobalt:



I felt given the size of the cage it would be difficult to fit the metal atom inside it and hence thought that it might be off-centred as shown in the image above.

So, it would be helpful if you could clarify whether my reasoning for the inability of $\ce{NH2NH2}$ to chelate is correct or not and why is it not possible for $\ce{N(CH2CH2)3N}$ to undergo chelation? Further, it would be helpful is you could tell why is there a contradiction between the book's statement and IUPAC definition? Is the statement from the book incorrect (because IUPAC can't be incorrect)?
My copy of Concise Inorganic Chemistry, 5th edition (J.D.Lee, Wiley publishers)1 has nothing contrary to say about hydrazine or 1,4-diazabicyclo[2.2. 2]octane (henceforth referred to as DABCO). It is most likely that the author of your adaptation has used his liberty to add these facts in your copy.
This then raises the question: is the author correct? Hydrazine derivatives such as Benzhydrazides and Salicylhydrazides 2 have been proven to show chelation. Pure hydrazine, however, is unlikely to show chelation due to excessive ring strain. Also, no literature has been found which shows hydrazine undergoing chelation. DABCO, on the other hand, forms complexes with Mercury halides3 with a denticity of 1. This ligand also does not show chelation, and fitting a large metal atom even off-center is highly unlikely due to large steric hindrance and the geometry of the lone pair, which is perpendicular to the structure and not favourable for chelation. Most complexes formed by DABCO tend to be linear in nature4 and no rings are formed.
In short, the author is correct in stating that hydrazine and DABCO do not form chelates.
EDIT: You may also want to read more on a class of compounds called Cryptands, specifically Cryptand-222. This compound displays the 'cagelike' ligation you were looking for in DABCO.
References:

Lee, J. D. Concise Inorganic Chemistry. 5th ed, Wiley publishers &amp;
Blackwell Science, 1996.
Issa, R. M., et al. Coordination compounds of hydrazine derivatives
with transition metals. I. Metal Chelates with Benzhydrazide and
Salicylhydrazide. Zeitschrift fur anorganische und allgemeine
Chemie, vol. 354, no. 1–2, Sept. 1967, pp. 90–97.
doi:10.1002/zaac.19673540118.
Shan, Zeng-Mei, et al. Synthesis, Crystal Structures, and
Characterization of Three Mercury(II) Halides Inorganic–Organic
Hybrid Compounds with 1,4-Diazabicyclo[2.2.2]Octane Ligand.
Inorganica Chimica Acta, vol. 366, no. 1, Jan. 2011, pp. 141–46.
doi:10.1016/j.ica.2010.10.023.
Thorp-Greenwood, Flora L., et al. Three-Dimensional Silver-Dabco
Coordination Polymers with Zeolitic or Three-Connected Topology.
Crystal Growth &amp; Design, vol. 14, no. 11, Nov. 2014, pp. 5361–65.
doi:10.1021/cg501231v.