This is not something I am aware of or have experienced. My standard RW contact forms, for instance, send to gmail addresses. The major trouble I can see is when the FROM field is overwritten when sending mail. If the mail doesn't originate from the server associated with the email address in the FROM field then it can be considered spam. For instance, if you set the From to your gmail, your shared host will never match as being associated with gmail.com.
Using smtp doesn't ensure a message can or will be delivered to a gmail or any other address. It just means that you're passing the burden of email deliverability onto the smtp server you're connecting to. If the reputation of that smtp server is bad, you're not getting a message delivered.
The easiest work around is to send a message to a local email address on your shared host then use gmail's imap/pop fetch feature to import the message. Bottom line is email deliverability is harder than you'd think. I'll follow up with you as soon as possible with your existing ticket.