This is a design decision in multi-tenant databases. With "root" tables, obviously you have to have the user_id. But in the non-"root" tables, you do have a choice when you are using surrogate PKs.
Say you have users with projects and projects with actions. Projects obviously has to have a user_id, but if actions are tied to one and only one project, then the user_id is redundant, and also violates normal form, since if it was to move to another user's project (probably not likely in your use cases), both the project FK and the user FK would have to be updated. Typically in multi-tenant scenarios, this isn't really a possible scenario, and so the primary key of every table is really a combination of tenant and a unique primary key "within" the tenant (which may also happen to be globally unique).
If you use natural keys extensively in your design, then clearly tenant+natural key is necessary so that each tenant's natural keys can be used. It's only when using surrogates like IDENTITY or GUIDs or sequences, that this becomes an issue, since it is tempting to make the IDENTITY the PK, after all, it is unique by definition.
Having the user_id in all tables does allow you to do certain things in views to enhance security (defense in depth), giving you a little bit of defensive programming (in SQL Server you can restrict all access through inline table valued function - essentially parametrized views - which require the app to specify user_id on every "table" access), and also allows you to easily scale out to multiple databases by forklifting everything on shared keys.
See this article for some interesting insights.
(In a massively multi-parallel paradigm like Teradata, the PRIMARY INDEX determines the amp on which the data lives, so I would think that this is a must to stop redistribution of rows to the other amps.)
In general, I would say you have a tenantid in each table, it should be the first column in the table, in most indexes and should be part of the primary key in most cases, unless otherwise justified. Where possible, it should be a required parameter in most stored procedures.