Usage of TFA in Pfitzner-Moffat oxidation and Collins vs Jones oxidation
Moffat &amp; Pfitzner have accidentally found their famous oxidation while working on mono-nucleotides (acually 5'-phosphates). Breifly, when pyromidium thymidine-5'-O-phosphate was reacted with dicyclohexylcaebodiimide  in anhydrous DMSO at room temperature resulted a violent reaction to give 90% of 5'-aldehyde product (Ref.1). They further pursued this finding and published their finding as specific reaction (Ref.2). The acid they have used in first finding was anhydrous orthophosphoric acid, which have given 90% yield. Hence, it is not necessary to have TFA as the acid. Following is the suggested mechanism for Pfitzner-Moffat oxidation: 



About Collins vs Jones oxidation, both of them used chromium-based oxidants. Oxidations with chromium oxidants proceed through a similar mechanism. Different between Collins and Jones are conditions: Anhydrous (in pyridine/$\ce{CH2Cl2}$) vs aqueous (use of $\ce{CH2Cl2}$). Following is the suggested mechanism for chromium-based oxidants:



After first oxidation to aldehyde, chromium oxidant needs $\ce{CH-OH}$ part available to further oxidize to carboxylic acid (see in both mechanism, how oxidation initiated and finished). In anhydrous conditions, this feature is lacked. So, oxidation stops at aldehyde moiety. However, trace of water make aldehyde in equlibrium with its gem-diol moiety, which gives the necessary requirement of $\ce{CH-OH}$ feature. So, in Jones oxidation condition, oxidation will further continue to give carboxylic acids.

References:


K. E. Pfitzner, J. G. Moffatt, “The Synthesis of Nucleoside-5' Aldehydes,” J. Am. Chem. Soc. 1963, 85(19), 3027-3027 (https://doi.org/10.1021/ja00902a035).
K. E. Pfitzner, J. G. Moffatt, “A New and Selective Oxidation of Alcohols,” J. Am. Chem. Soc. 1963, 85(19), 3027-3028 (https://doi.org/10.1021/ja00902a036).