"But now it is possible to go directly from a trainer and second plane, to a turbine without actually having any knowledge about them or how they are built"

Its not, that's one of the reasons why the AMA has a requirement for you to have a Turbine wavier, and in order to get that you have to go and get 2 CD's of which one has to be an JPO CD to sign a wavier that states they have seen you fly an aircaft that is capable of flying to 150MPH, along with a bunch of other things need to be signed, these people (CD's) are very experienced when to comes to building or flying a jet. I don't think any CD would sign you of until he or she see you fly and complex aircraft and that you show you know what your doing and can fly the aircraft safely. Go to www.jetpilots.org you can read about all the requirments to fly a turbine jet

Now if you fly at a non AMA field you can fly a turbine jet with even having flown a trainer, but a very foolish move and would be putting not just yourself in danger but everyone else around you, second you probably would not have a have a jet for a very long time due to no experience and be probably picking up....no digging up pieces from your jet that just went into the ground at a very fast speed.