As with a lot of things, "Hash Matches are often better than Loop Joins" has caveats. For small tables a Loop Join may be better, particularly if the inner loop is very small (only a few rows). It would be handy if you had some of the logic or the two execution plans to do comparisons. Given the view is encrypted, I take it this would be difficult to arrange. Could you get a copy of the T-SQL Code and generate the execution plans?
You could try putting in a query plan guide that automatically adds the option, but without some more information around this it's difficult to give more feedback.
Nothing in life is ever so complicated that with a little work it can't be made more complicated.