Typically they shouldn't. However, there are some menu  items which also
require certain client-side programs to be installed like the ones that
use the Office client integrations.

That makes sense, but the strange thing is that the same individual has "edit in
MS Word" in same items, and it doesn't have on other items inside the same
Document Library.
Person A – has XP, office 2003 and Full Control to the site and DL: the accesses
were given in SharePoint2003 before migrating to SharePoint2007 – everything
works fine.
Person B - has XP, office 2003 and Full Control to the site and DL: the accesses
are recent and were given directly in SharrPoint2007: not all documents have the
options "Edit in MS Word" and "check out". And, if you click directly on the
document name, the document  opens as "read only".
1. First I asked Person B to login in Person A computer – same behavior (so it's
not a PC issue).
2. Then I asked for Person B to login in a computer with Vista and Office 2007 –
same behavior (not a version problem)
3. Then we created a new XP machine, with Office 2007 and created a new and
clean profile for Person B - same behavior, again.

I don't have any more ideas - do you think you can help on anything?

You mention full control on the site - what about the document  library
and/or the individual documents? Are you sure there aren't library  or
item level permissions in place?

yes, I am sure there is no DL or item  level permissions.

the DL inherits its permissions from the site and the items inherit from the DL.