Thank you for your post.
I am unable to duplicate the problem. I receive the same messages as you, but after I resize the column and answer "Yes", the columns resize properly.
Try creating a new database file with one field. Make it available for network sharing, go to another machine, open the file remotely, switch to Table view and resize the column. Does this work? If so, then the other database file may be corrupt.
Any additional information you can provide may be helpful in determining possible causes.
I believe there may be two issues at work here ... when a file is served and you move a column on a table, FM will ask if you wish to keep those changes, since it could affect design and display for all users. It probably then won't change because you have reached the maximum width for your table and, when you attempt to move a column, FM must have that extra room FIRST to move the column.