Memory limitations on interfacing SD Card with 4-bit SD data transfer mode
No, that's nonsense. SD and SPI modes can both be used to access data on any size of card.

What is true is that SDHC cards (that is, SD cards larger than 2 GB) must be initialized differently than plain SD cards (2 GB or less). However, this is true no matter whether you're using the SD interface or SPI.