I suspect is it somewhat legit, simply because you rarely see people complaining once such facilities are built and operational.
A lot of people claimed that the public would immediately vote out of office the Hennepin County commissioners and state representatives that pushed through the Target field deal, but that didn't happen. Many of those people are still in office today. People have short memories when it comes to these things, for better or for worse.
The only instance I can think of where that did happen, was with the representative that cast the deciding vote to pass the tax hike that built Miller Park in Milwaukee.
The biggest issue with using public money for an NFL stadium, as opposed to a MLB stadium, is that the football stadium is more expensive, yet is used for 10% of the dates, making it a much worse investment. By building a covered stadium, you're able to use it year-round for other activities, though this is overblown to a large extent, simply because the Metrodome isn't really used that much outside of Vikings games and Gopher baseball.
One note about the Metrodome, is that not only was it built on the cheap, it's had very few renovations in its 30 year lifespan. In fact, for as much use as it's had, it's had fewer improvements than most buildings of its type. Look at the Ed Jones Dome in St. Louis, built in 1995 - they just did a 30 million dollar renovation on the stadium last season. Look at Target Center even, built in 1991, which has also had extensive renovations. The dome simply has not been improved or kept up, and as such, it should be no surprise that issues are starting to pop up.