In answer to you quesion, yes he is right.
Linux and similar operating systems have significantly more functionality and a lot of it is started at boot time since memory is hardly 'scarce'.
Also 'your applications' as you call them do a lot less so that is why they start up quicker.
If you could give us an example of an Amiga application and a PC (Linux/Windows etc...) application that have the same functionality yet different startup times we could make a decent discussion of this.
I'd appreciate it if you could provide a link to the forum where you posted it, would be interesting to see.
//edit : I found it anyway : http://forums.suselinuxsupport.de/in...howtopic=60981