A "synced" or synchronised tree with FTM 2012 can be public or private, see other discussions on the forum re: public vs private trees. You are in full control of this. Having an internet link means you can have the program auto search for you this makes finding new sources of information dramatically easier although of course you need to check the sources and not just rely on other information but the fact that you can get automatic searches of military, parish, overseas, transportation, medical, school etc records many of which you'd probably not think to search should surely make your research easier?
There are of course plenty of out of date programs out there many of which are so old they pre-date the popular use of the internet and will last a short while with no support and no clear upgrade path. So you can easily go for an older option if you don't mind your research taking a lot longer and risk having the tree stranded in an old unsupported version of a program.
Almost all programs these days will use the internet to assist speeding your research. Using an ancient version of a program might seem like a good idea to avoid the internet but comes with the potential of a whole lot of incompatibility problems for the future.