Service Content Pack
It is possible in Power BI by developing an online service content pack. This allows online services to give their customers insight into their own data via the PowerBI.com cloud service. The ISV pre-builds the data model (and some initial charts); the end user doesn't have to worry about joins at all. They can drag & drop the fields that the ISV makes available.
There are some base requirements (it has to be a SaaS application that has an API accessible via the public internet).
More information: https://powerbi.microsoft.com/en-us/documentation/powerbi-developer-content-pack-overview/
Embedding
If the ISV is building their own portal, they can embed SSRS reports on their own website (and use parameters that pass the customer ID from the website directly to each report). This looks like a good place to start: https://learn.microsoft.com/en-us/sql/reporting-services/application-integration/integrating-reporting-services-into-applications. One downside to this solution is that SSRS doesn't allow the end-user to change the reports themselves (no dragging or dropping fields).
You can also embed Power BI reports onto an externally facing website. More information here: https://powerbi.microsoft.com/en-us/power-bi-embedded/
There may be other solutions, such as tools that allow external access directly into SSAS, but I've limited the scope of my response to the two tools you've asked about (SSRS and Power BI).