Only sort of true. The earlier Android phones had a very small amount of internal storage, and so yeah, most of them shipped with an SD card of some sort.
That is TOTALLY optional, and it's also not even close to being necessary to emulate the SD card. App installs look for SD storage for some things, but that's always optional.
The main reason SD card emulation is still done is USB Mounting. If you have an SD Card, it's formatted in FAT32 (the SD Card Standard), rather than ext3 or ext4 or whatever Android is using internally. Which means the card can easily be mounted as external storage on a PC. That works on pretty much any PC, even Macs, as well as other things... you can put this kind of storage on a PS3, another Android tablet, etc.
If, instead, they go with a single volume (as my Galaxy Nexus does, for example), the device has to connect using a higher level, network-like protocol such as MTP. MTP used to be kind of a special agreement between Windows Media Player and your device. These days, it behaves as a first class drive mounting means within Windows, but it's less compatible with other systems. On the plus side, since it's by nature a higher level, networking style protocol, you don't have to unmount the volume on your phone to mount it on your PC.