Yeah, indeed, 4...dxe4 has the best engine evaluation though 4...d6 was played more often. 5...d6, 5...Nf6 and 5...Ne5 seem to be good moves.
Terminological remark: 4. d4 may be considered as the transition from Italian Game: Hungarian Defense into Scotch Game. 
It seems that Black is OK if he plays this:
When White plays 4.d4. If this is actually an inferior line, is there an explanation for the much better database score?