I'm inclined to believe this is just typical ignorance on the police's part concerning how dangerous places like Albania really are. I've been to Albania and there's nothing remotely dangerous about it - a few landmines left over from the war in some specific places that are at the opposite end of the country to Vlore and that's about it.
Anyway, the easiest and cheapest way that I can see to get to this game is to get a cheap flight out to Corfu (right next to Albania and lots of flights available at this time of year) and then get a ferry to Sarande which is a bit down the coast from Vlore. There's a ferry every day from Corfu to Sarande, it takes 30 minutes and costs about 20 Euros. From Sarande it's simple enough to get a bus or one of the private minibuses everyone uses there (furgons) to Vlore. You don't even need to stay in the place, which is just an industrial port town and can stay in Sarande instead (which is quite nice) or even Corfu itself (many people make daytrips to Albania from Corfu). If you find a cheap flight to Corfu then it won't be that expensive at all.