That is an urban myth relayed by people who weren't even using Ubuntu in its early days.
Other distros were as easy to install as Ubuntu even before Ubuntu was founded. Besides Ubuntu was using the then experimental debian installer you could already use with a regular debian. They just shipped it on the default CD image earlier than debian did.
What they did to be on top was using Mark shuttleworth's money to ship an insane amount of free install CDs to anyone asking for them which meant that for a small period of time, when most people were on dial up internet ISDN and shitty ADSL, Ubuntu went suddently to be the number one distro installed. A friend, family member or coworker was curious about Linux? You'd hand him one of the fifty Ubuntu CDs you had lying around. I know I was one of those handing out CDs left and right. It was a time when to get an install CD without broadband you'd have to buy a magazine, and you didn't get to choose which distro was featured each month, a book or a boxset (not available everywhere). Later all those many early ubuntu adopters became ubuntu evangelists.
But bar a few exceptions like slackware, debian with the default vanilla installer or gentoo, there was nothing particular about the ubuntu install experience compared to other distros. Mandrake, Corel Linux ans Xandrows for example provided super easy install experience even before Ubuntu became a thing.