No — they measure different things, and both can be true at once. Y-DNA follows one single line (your father, his father, and so on) back thousands of years, so it’s very specific but represents only a tiny fraction of your ancestry. Ethnicity/ancestry percentages (“% Italian,” “% Mediterranean”) come from autosomal DNA, which blends all your ancestral lines over roughly the last few hundred years.
A paternal line that traces to one region and an ancestry estimate that points to another are not in conflict — they’re answering different questions.