From some people when I receive a meeting request it comes through as a
regular e-mail, from other people it is processed correctly as a meeting
request, prompts a response and is added to my calendar.

For example: I send a meeting request to "Joe" he receives a proper meeting
request. But when Joe sends me a request, I receive a regular email.

When I send a request to "Tom" it works properly in both directions.

Joe is sending from a large company with servers, etc. Tom is sending from
a stand alone computer.

Any thoughts about what is going on here?