No, what happens is as follows. The person wanting to schedule a meeting goes to Doodle and causes it to send an invitation to the persons that will be attending the meeting. The invitation consists of an email-message containing a link. Clicking the link opens a diary-like page with tick-boxes to indicate which dates and times are acceptable to whom.
It is the invitation that I am unable to see in Safari. If you are prepared to let me have an email-address for you, I shall see if I can manage to send you such an invitation -- to an imaginary meeting, of course --- using Opera.