Oh bollocks to that. Therapy appointments, like any other appointments, are at a set time. Given variability in traffic, parking, and other unexpected delays, or the vagaries of the bus system, most people will need to build contingency time into their journey. Generally, unless you live very close, you have to choose to either time it so that you're usually early (and occasionally delayed but on time), or so that you're usually bang on time (but occasionally late).
Quite apart from not wanting to be rude by being late, and wanting to make the most of my therapy session rather than feeling rushed and stressed, I'm probably paying £1–£2 per minute for this person's time, so I don't ever want to be late.
Most decent professional therapists will have somewhere you can wait until your appointment time, just like a decent professional solicitor or a decent professional podiatrist. No need for separate waiting and leaving areas — they don't have that at the GP, the solicitor's, or the CMHT.
I have occasionally seen therapists who had no waiting area — one working from a private house, and one working from an office in a small business estate. It would be ridiculous to expect a client to either magically turn up at their precise time every week, or to hang around on a random street corner in the rain until the dot of 3pm, so generally they scheduled their appointments and any writing-up time so that if necessary, they were ready to let you in up to ten minutes before your time (and either start early, or fill time until the start time). Even so, it was a worse overall therapy experience from the client POV, IMO.
Sometimes, the person driving me was able to stay while I waited in the car, but that's not ideal — some people, including me, benefit from a few minutes in the waiting area before their appointment starts, to transition out of "world" headspace and into "therapy" headspace. It's normal for therapists to have a waiting room, and usually to furnish it with this in mind. Therapists who don't create a comfortable environment for their clients, including a calm waiting area which allows clients to arrive in plenty of time and mentally ready for their appointment, should accept their responsibility to compensate for the lack of waiting area by making it very clear what the arrangements are, and not running clients back-to-back.
Assuming you weren't literally banging on the door of the consultation room knowing that another client was in there with the therapist, it is absolutely not a boundary violation to turn up ten minutes before your appointment time. Your therapist was just taking advantage of your unfamiliarity with therapy in general and her setup in particular, to try and disavow her own responsibilities and make you think you made a faux pas. Ten minutes early for an appointment? Boundary violation my arse. It's normal, polite, considerate behaviour.