Your "experts" are correct. Flash Video streams by nature so no streaming server is needed. It uses progressive download through HTTP. You just need to use a Flash video player. The only time you would need a streaming server would be for a live broadcast. This is the main strength of Flash IMO. I use it mostly for video with an occasional small embedded animation. I never do full Flash sites or Flash navigation.
Flash is really not bad at all if you know how to use it so that it doesnt hamper your SEO and navigation. Those who say otherwise is selling HTML.
Yeah, I still use flash somewhat, but overall its rare. Usually for some type of slideshow or presentation that is not achievable elsewhere. I'd definitely lean for it being more of a last resort though