This exactly. It IS easier because when it comes to a new company, you've only got one problem - the salary. When it comes to your existing company there are two problems. The money, but also the fact that you're having to ask for it. The more you deserve it the more awkward the conversation becomes since the ask itself is evidence of a management failure. In extreme cases, making the request can be as uncomfortable as having to reapply for a job you've already got.
In a well-run shop, managers have a very good idea as to who is worth what, and how much the company stands to lose if they lose good people. Staying one step ahead of this curve is a fundamental part of their jobs as a managers.
Obviously, the rules are a bit different in an early-stage start-up where the founders are doing everything at once and hoping something connects. But once an operation has hit cruising altitude, you really shouldn't have to ask for a raise if you're actually worth what your asking.