If one wants to take an interest in when and how certain Y dna haplogroups arrived in Italy that is all fine and well, but attempting to quantify ethnic makeup with Y-DNA is a widespread fallacy.
If well done, Y-DNA can be used as a proxy ... a noisy one, but still a proxy (that is only usefull when later admixture event have blured the autosomal DNA ... an issue "easy" to alleviate with ancient samples admixtures, but sometimes we don't have a lot of samples for many reasons).
The first thing to do for such analysis is correct for post-merging founder effects.
If you absorb diverse Y-DNA from foreign regions, you will also absorb admixture (less than Y-DNA if the migration is only male-mediated).
What should be looked at is the number of clades "already defined" at the moment of the claimed migration (in order to erase the impact of founder effets).
Then you can correct for sex-biased migrations if it is needed for the concerning movement.
Basically, under the assumption of similar clade-survivance rates post-population merging (which is a descent hypothesis), you can make an estimation of the fraction of males having contributed to the merged population.
Of course, there is some movement that can't be traced with such proxy, for exemple autosomal diffusion through mating network involving women migrations.
This is a very descent proxy of admixture, but it can be noisy (in particular when big founder effects have erased nearly all the older diversity dating from the pre-merging populations). That's why reaistic error bars also need to be produced and the conclusion need to rely on a significant number of independent clades by the time of the claimed population merging.
It also require a good spatial sampling of the concerned populations to avoid "local" peculiarities (associated with a specific site/region).
No, it is not a "fallacy", just a proxy to be used carefully and with properly assessed error bars ... as any statistical estimator.