No, this is not true.
the validation needs to happen on the forms action page.
your form is set to post to itself, so the validation needs to happen on the same page as the form.
open the server behaviors panel, and double click the Server Validation behavior to edit it and add additional validations.
select the validation type, click the lightning bolt next to Server Variable and select the form element to validate, then click the plus button to add it to the list.
repeat until you have set all of the validations and click OK.