No, in your proposed case, a single blockchain would be better than many. If one party controls the whole blockchain, it's "easy" to forge data in it [1]. On the other hand, distrust between involved parties makes it hard to forge and deny actions on a single blockchain (though it'd still be possible with a 2-party system). Btw, I wonder how and why people want to implement blockchain for use in government or banks - since they are big monoliths, 51% attack is a real possibility.

[1] http://www.investopedia.com/terms/1/51-attack.asp