It would be impossible to successfully fabricate scientific data on that scale for any length of time...
And there are plenty of observatories that could simply look at it and see that its not performing corrections to stay in L2- L2 is a point of UNSTABLE equilibrium.
Imagine a marble inside a bowl... it will stay in the bowl indefinitely unless a large amount of energy is imparted to it- that is the situation satellites that orbit the Earth are in...
Now, turn the bowl over and balance the marble on top- it can be done, but its not stable. Now add a oscillating fan pointing at the bowl... this is the situation the JWST is in- the fan is the solar radiation pushing on its huge sunshield. To keep the 'marble' balanced you are constantly having to put energy into the system to keep it balanced.