how could a 3 amps transformer deliver 3 amps after filtering?
Just a few points for clarity.  The transformer's voltage will drop if any load at all is added.  The rated current is the current at which the transformer will give it's rated voltage output.  For instance, I recently bought a +/-12v center tap transformer to build a benchtop power supply and it actually has a no-load voltage of 36V.  

Second, be aware that RMS voltage and current do not represent the same energy delivery as an equal voltage DC.  An equal RMS voltage means that the circuit will produce equivalent ohmic heating(power loss) to that voltage in DC.

From that fellow's project, it doesn't seem to be clear whether he has tested his PSU at 30V and 4A continuous.  There is a chance that running it continuously would burn out the transformer.  That being said, a transformer's durability ratings relate to not going over the insulation thresholds and not running at a current that will cause it to overheat.  It is quite possible that the PSU exceeds the rated load of the transformer, but not the safety margins, whatever they are, built into the transformer, and as a result, runs at greater than it's rated load.  He is also using a fan in his case, which may be keeping the transformer cool enough not to thermally cascade, the same as you can run greater than AWG rated current on just a copper wire so long as you cool it well enough, and have to derate it (consider it to be able to carry less current) when it will be exposed to higher ambient temperatures.