I think more precise language is warranted here. If you're vaccinated, you have a reduced risk of becoming infected if exposed. The protection of the vaccines against infection, however, appears to decrease fairly rapidly, hence the discussion around boosters.

But if a vaccinated person (especially one who has lower neutralizing antibodies) puts themselves in environments where they inevitably have more exposures (think crowded, poorly-ventilated indoor spaces like bars) and they are not as vigilant about mask wearing, they might have a relatively higher risk of getting a breakthrough infection than even an unvaccinated person whose behavior leaves them with fewer exposures.