This is ksh working as intended. The "." or dot builtin performs a PATH search and a .profile file has not been found in any PATH directory. Someone thought that a PATH search was the correct thing for the dot builtin to do, so here we are.

The source builtin comes from a different shell, csh, though has been pilfered into various modern bournelike shells. But maybe not various ksh flavors. Modern is a perhaps dubious term given that some bournelike shells such as ZSH date to 1990. Remember Yugoslavia?

Anyways, the dot builtin needs a fully qualified path to not do a PATH search, similar to using a fully qualified path to a command. A more correct way to load ~/.profile in a ksh would run along the lines of the following.

But the documentation is long and I don't want to read it

also they're having this sale on power converters at Tosche Station

Use process tracing. This may also help in the fairly common case of there not being documentation or the documentation sucking. A string that is easy to grep for can help filter out noise.

Someone looking at the trace results would need to know enough about unix to recognize that a PATH search was being done. This may help narrow down what to look for in the documentation. Searching only for paragraphs that mention "PATH" yields much less to read: