If a long-term owner told you that, by all means consider it; if a non-owner (including a mechanic) tells you second/third-hand horror stories, Iād be pretty inclined to ignore them.
Like so many things these reputations form for good reasons - you may get lucky and have no particular problems with an individual example but that doesn't mean the reputation isn't deserved.
As (by now historical) anecdata I owned an Alfetta (2000, gasoline, "America") for several years (used 50% with my father) we made 250,000 km with the original engine, then we put an used (from a wreckage) one with alredy 66,000 km and drove it for another 100,000 km or so when we had an issue with the gearbox/transmission and the car was overall too old to be worth the repair, but the body was in very good condition (car was around 15 years old).
Later I drove for a few years a 75 (bought used with already 90,000 km, "italian") and while I had no particular issues (engine and mechanics in general) up to the 150,000/200,000 km, the body had lots of issues with rust/corrosion after 6-7 years.
I would not call any of them "unreliable", they needed some little maintenance, but I would say no more than other make/models of those years (those were the '80's and early '90's).
Later Alfa Romeo became essentially "FIAT with another name" and reliability was essentially the same as the FIATs (rather poor, but not as bad as they are sometimes depicted).
Not to say the cars are perfect, but most owners end up with relatively hassle-free ownership experiences these days.