Email to Case Premium and Partner/Customer Portals and Communities
Partner/Customer Portal and Community users cannot use the New Comment page in Email to Case Premium because that license type does not have Create access on the standard Email Message object.
The E2CP new comment page performs 3 operations at once: 1) add a comment 2) update Case fields and 3) send an email which gets stored in the standard Email Message object that Salesforce provides.
The Customer Portal/Community and Partner Portal/Community license types do not have Create access on the Email Message object and therefore an error will occur:
Sending e-mail with new comment failed: Insert failed. First exception on row 0; first error: INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY, insufficient access rights on cross-reference id: 
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