Even worse, typerwriters of the day were awful. They dropped, slanted, missed, and generally had impurities in the final product -- even the vaunted IBM with the typeballs. To exactly match a document produced in that era would take hours -- shifting over to the right a point, dro;pping a letter a 1/2 point, etc. etc.
To do it in 5 minutes PERFECTLY is/was proof. Only modern printers can produce a document with perfect spacing, sizing and kerning.
The "documents" are sufficiently munged by faxing and crumpling that it's not clear that any defects that would have been present in typed originals would be identifiable in the faxes. Had the documents been set in a monospaced computer font whose horizontal and vertical spacing were 0.1" and 1/6", respectively, and had the typist been careful to avoid any "Word-isms" (superscript ordinals, etc.), it could have been harder to identify them as fakes.
The problem here is that unlike monospaced fonts whose letterspacing can be described using two numbers (horizontal and vertical, global for the whole font) getting the spacing right for a proportionally-spaced font requires many dozens of numbers. The likelihood of all of those lining up on two fonts would be exceptionally remote unless one font was designed to precisely match the other, or both were designed to precisely match a common "ancestor". Since Times New Roman was not designed to precisely match any pre-existing font, the "documents" must have been created to precisely match Times New Roman's spacing.