Bitcoin addresses carry a checksum to make reasonably sure that an address isn't mistyped when money is sent to it.

There are 4 Byte of checksum data in an address. 4 Byte = 32 bit. The checksum can be assumed to have equal distribution. This means that there is a 1 in 2^32 chance that a mistyped address is valid, so 1 in 4'294'967'296.

It is very unlikely that the mistyped address is correct and no wallet will send money to it because it's invalid. If you are not the 1 case in 4'294'967'296 where a mistyped address is actually valid, you're being defrauded.

You can find out whether the address they allegedly sent the money to is valid by entering into blockchain.info's search box. Enter the address with the type into the search box on https://blockchain.info (not the one in the top but the one in the center/bottom (depending on your screen's size) right).

1PKjFveyaLz5vzKHjfYBjjLiTEQLXfqL6p is a correct address and blockchain.info shows us that it never received a transaction. If we swap out the p in the end for a q, we're only shown an error message:

Unrecognized search pattern

This is because the address with the typo is invalid.

amaclin's answer (you are being lied to) is overwhelmingly likely to be correct.

Speaking purely theoretically, I don't think the 32-bit Bitcoin address checksum guarantees catching all one-character errors. So there is a tiny chance (about 1 in 4 billion) that the "q" address is actually valid. You can easily check this by looking up the "q" address on a a block explorer site like http://blockchain.info or http://blockr.io. If the guy was telling the truth, it will show the address as valid and containing the appropriate transaction. Almost certainly it will instead show the address as being invalid, and then you will know for sure that he is lying.

But even if by some chance the "q" address was valid and the guy really did send the coins there, that doesn't really change anything. The fact that he screwed up and lost some of his own money doesn't change the fact that he still owes you, and you have every right to insist that he get some more money and pay you. Of course, you may or may not have any way to actually make him do it.