Yes, that's true.
Despite the fact that I happen to eat mostly vegan food myself, I am extremely skeptical about the claims of most such studies that claim positive results for vegan diets, because, as you say, they lack adequate dietary controls that would enable the interpretation of the results.
I looked in the paper at "Materials and Methods", but there was no useful information about the actual diets, because it sent the reader to some older papers, where supposedly the diets were described.
I went to one of the referred papers, and there the description was equally useless, because there had been no strict controls. The participants were given guidelines about what they should eat and an example recipes book and then they provided weekly reports about what they had eaten.
This is not good enough to know with any certainty which are the components of the diet that had the observed effects.
Typically, the so-called vegan diets are healthier diets than what most people eat, for other reasons than for not including substances of animal origin.
None of the dietary studies that I have seen has provided any conclusive evidence that meat per se is the harmful ingredient, and that the differences in outcomes are not caused by other factors, e.g. inappropriate proportions between protein, fat and carbohydrates, too many calories, too much animal fat, unhealthy methods of cooking, like frying, unnatural composition of the food ingredients of animal origin caused by industrial farming methods, e.g. excessive amounts of hormones, vitamins, antibiotics etc., and so on.
>None of the dietary studies that I have seen has provided any conclusive evidence that meat per se is the harmful ingredient
This is innacurate if not simply false; according to the WHO red meat is a class 2 carcinogenic and sausages are class 1 carcinogenic. This leaves only white meat as non cancerogenic
If you look at the data vegan (and vegetarian to a lesser extent) diets over various studies consitently perform better in cardiovascular health and cancer rate (colon in particular) compared to the omnivorous conterpart
Those mentioned by you are very specific kinds of meat, and there were doubts about how healthy they are long before the last century.
There is absolutely no evidence that any data about red meat or sausages also applies to other kinds of meat, e.g. those that have negligible content of myoglobin and saturated fat, like poultry breast or white fish.
I agree with what you said, that almost any study about vegan or vegetarian diets shows positive effects, but it is never clear which are the differences from the comparison diets that really mattered, because the compositional differences between diets were too many and too variable.
The OP is actually talking about the studies that the WHO was using to classify meat as a class 2 carginogen. For meat preserves the evidence is clear and known mechanistically, but for meat in general it's inconclusive at best and badly-designed at worst.