In some instances an email may show as read by your customer but could be reported to you as not delivered.
The reason for this discrepancy is most likely the result of one of two things. 1) Your customer has virus/spam checking software loaded set up on their email which scans the email before delivering it to their inbox. This type of checking software will cause the email to be reported as read. 2) Your customer is using a program such as unroll.me which takes all their emails and filters them into a single email and stores them for them rather then delivering them to their inbox.
There are two places you can check if an email was delivered to your customer.
1) If you go to their contact page and scroll down you will see two boxes one will list all emails they have ever been sent and the other will show all activity connected to them including when emails were sent, opened, and if links were clicked on.
2) Under communications in your side bar you will see a deliveries tab which gives you a running cumulative list of all emails that have gone out and who they were delivered to. You can search for your customers's name in the list and see what emails they received.