Relative acidity of acetic acid derivatives with strongly withdrawing substituents
Some cheminformatic descriptors for the puzzling compounds can be found on the PubChem website:

SMILES    N+(=O)O ;
Nitroacetic acid; 625-75-2; alfa-Nitro
acetic acid; 2-nitroacetic acid; ALFA-NITROACETICACID;
CID: 43581;
MF: C2H3NO4;
MW: 105.05g/mol;
InChIKey: RGHXWDVNBYKJQH-UHFFFAOYSA-N   ;
IUPAC Name: 2-nitroacetic acid   ;

and

SMILES N+(C)(C)C;
TRIMETHYL GLYCINE;
N,N,N-trimethylglycinium; Cystadane;
CHEBI:41139;
carboxy-N,N,N-trimethylmethanaminium;
CID: 248   ;
MF: C5H12NO2+   ;
MW: 118.15g/mol;
InChIKey: KWIUHFFTVRNATP-UHFFFAOYSA-O  ;
IUPAC Name: carboxymethyl(trimethyl)azanium

With glycine betaine it is usually meant the chloride salt, which would result in chloride counterions. For dilute solutions presumably those chloride ions don't matter, but they would at higher concentration.
Nitroacetic acid even has its own Wikipedia page. The acidity reported there is pKa 1.68, which is similar to that found in other sites such as in ChEMBL, pKa 1.75.
Glycine betaine or trimethylglycine also has Wikipedia and ChEMBL entries. From Wikipedia, acidity (pKa) is 1.84. From ChEMBL, 2.26.
So from this data alone it would certainly seem like the book is correct. Still, those pKa values are very very similar.