Do update permissions require select permissions

I have run across a problem while creating a database with row level
permission
checking via views and triggers. The just of which is update does not
work
for a user unless they also have select permissions. Select
permissions are handled with a view, while insert, update and delete
permissions are handled via triggers.

The simplest table which demonstrates the problem is:

create table data_t (id int4, stuff text);
grant insert,update,delete on data_t to public;

As the table creator issue the query:

insert into data_t values (1, 'Some stuff');

Now as some other user one can do:

update data set stuff = 'other stuff';

And it works okay. But the following fails:

update data set stuff = 'yet other stuff' where id = 1;

Why is this?

The reason that I need to not let the user have select on the table is
that
they are only allowed to select certian rows and there is a view that
takes
care of this. For insert update delete there are trigger functions.
I know that rules on the view would handle the problem but I am using
inheretence and the query plans grow to over 270 rows when rules on
views on
base tables are put together.