Did apple claim to invent it? I think their claim to fame was that they were the first to popularize the PC. The first to build an empire based around the PC.
No, Apple never claimed to invent the personal computer. The Apple ][, along with the TRS-80 and the Commodore PET all came out in the same year (the "1977 Trinity"), so it's not really right to say they were the first to develop a successful commercial personal computer.