This is not nearly as true as popularly claimed. Trade was far more widespread than popularly imagined, and the concept of "race" quite literally hadn't happened before the Spanish started shifting toward it during the Reconquista.
Genetic analysis has proven a maximum historical "immigration rate" between the general sub-Saharan African and European populations of under two people per generation, for, for all intents and purposes, "forever", with the rate being even lower (less than one) until quite recently in historical terms. This can be proven by neutral genetic drift models. This is the average value for Europeans
overall, although I
believe (I'm not completely sure) that it excludes populations derived from historical Arabic settlement in southern Spain and the Mediterranean islands (who are themselves largely genetically distinct from their natively European neighbors); the further north you go, the less gene flow there is. Essentially, different ethnocultural groups, even those living side by side, just categorically did not mix much until comparatively modern times - which is why we've retained distinctive groups like Sephardim, Basques, and even the Welsh (who are much closer to Anglo-Saxons, but still distinguishable) to this day.
Now, it's worth saying that the genetic evidence only tells you about who had surviving descendants, not the entire population, but you can compare this genetic evidence to historical evidence that tends to the same conclusion - for example, there are
no historically documented cases of people of sub-Saharan African descent in Britain during anything like the time period we're talking about, even though it would certainly be something people would find remarkable; and the ethnic distinctions they
did find worthy of remark also show that, to the British of the time, a noticeably "dark complexion" describes something like the Black Irish, who seemed dark enough to their countrymen to justify the name but are almost indistinguishably white to modern sensibilities. If they had experience with much darker complexions than that, it seems unlikely that they would think them any more notable than we do.
I don't think any soldiers got land in Italy by that point. Iirc veteran land grants were mostly given out from conquered lands, so people ending up in Britannia/Gaul/Hispania would not be improbable. There were plenty of land available there after the genocides after all.
On the contrary, the genetic trace of Roman invasion in Britannia is documented to be minimal. Hispania too, for that matter, but I don't really know much about Gaul. Quite the opposite of genocide, there is nearly complete genetic continuity between the pre-Romans and the immediate end of the Roman period (which in the Iberian peninsula, continues to this day with most modern Iberians being essentially Celtic except for aforementioned Arabic settlements, while the Britons were of course heavily mixed with Anglo-Saxons later, although considerable Celtic ancestry obviously remains).