It's probably not true.
There could be a variety of reasons why you haven't tested well in the past, but I do not believe, after years of teaching the LSAT, that there is no such thing as a fundamentally, permanently, "bad test taker." When people say "I'm a bad test taker," they usually really mean one of the following things:
"I got a bad SAT score because I suck at math." -- Okay, well, there's no math on the LSAT. Even the Logic Games, which seem math-like, are really just reading comprehension tests in disguise. (Read the rules, understand the rules, follow the rules to their logical conclusion.) If you're strong in verbal but bad at math, then the LSAT is the perfect test for you. (Certainly much better than the SAT, GRE, or GMAT.) Hopefully, the LSAT will teach you that you're a good test taker after all.
"I got a bad SAT score because I suck at verbal." -- This is tougher, because the LSAT is a brutally intensive test of your English verbal abilities. If you don't like to read, and/or if you have a limited vocabulary, then this just might not be the test (or field) for you. But I still don't think you're a "bad test taker." Instead, I think you have some weaknesses in your verbal skills that could begin to be addressed if you were honest about them.
The best way to get better at your English verbal skills is very simple: Read more! I don't care what you read, but you must read. Even trash is fine, as long as you're constantly reading. US Weekly? Sports Illustrated? Harry Potter? I don't care. In high school, I read every book Stephen King ever wrote, and it was a far better education than all my English classes combined. Just pick up something that will hold your interest and read as much as you can. It's going to take a long time, but eventually it's going to work.
"I get really nervous on tests." -- This one is very common, and very easy to deal with. In every class I offer, I administer a series of full-length, proctored practice tests. This gives students an opportunity to practice taking the LSAT in a very realistic testing environment. Through repeated exposure, the test-day jitters can be dramatically alleviated. Getting nervous doesn't mean you're "bad" at something. (I used to be the world's most nervous public speaker, but through repeated exposure I've actually come to love it.) I have a couple other strategies for dealing with test-day nerves--if you're worried about this, send me a note and I'll be happy to give you some additional thoughts.
"I have a learning disability/difference." -- Go apply to the LSAC for some accommodations. It's difficult, but it's possible. Unfortunately, even if the LSAC gives you extra time, your future employers and the courts you'll be working in are unlikely to do the same. Your opponents, if you're a litigator, will be doing everything they can to gleefully exploit your weaknesses. Law school, and real legal work, both require digging through mountains of written material, usually on deadline. If you're having a hard time with the LSAT because you have trouble focusing on written materials, then it's not so much that you're a bad test taker--maybe law just isn't the field for you. (Of course, if you really want to be a lawyer, then you can and will overcome this obstacle.)
"I'm just not happy with my current level of LSAT scoring." -- Yeah, I know. You haven't studied enough, or you haven't had the right instruction, or perhaps your verbal skills aren't strong enough (see above), or perhaps you have some jitters (see above) that you need to do something about. But you need to be honest, and stop reinforcing your bad performance with the weak excuse that you're "just a bad test taker." We can't address your real problems until you stop hiding behind the excuse.
It's definitely counterproductive.
I'm not going to go all new-age mumbo-jumbo here, and waste your time with a sermon on the Power of Positive Thinking, but I am going to discuss some very specific ways that saying "I'm a bad test taker" is hurting your performance.
It's preventing you from acknowledging your real weaknesses. -- Odds are, if you think you're a bad test taker then you probably fall into one of the categories above. As long as you keep saying "I'm a bad test taker" you're going to avoid addressing your real shortcomings.
It's making you think the test is harder than it actually is. -- I can't tell you how many times I've heard a student say "well I thought it was C, but that seemed too easy, so I chose D." This strategy of "doing the opposite" may have worked for George Costanza, but it's a tragically bad idea on the LSAT. You must be open to the possibility that some of the questions on the LSAT are actually easy! If you're constantly telling yourself that you're a bad test taker, it's going to be very difficult for you to trust your instincts and pick the obviously right answer. You can do this, but you do have to believe you can do it. Stop selling yourself on the idea of failure.
It's keeping you from studying. -- In my experience, people frequently lean on "I'm a bad test taker" to avoid explaining (to me, and to themselves) why they haven't done their homework and why they miss so many classes. My typical student studies for 20-25 hours a week for a period of 4-12 weeks, and sometimes as long as 6 months. As a result of all this hard work, my typical student improves their LSAT score by 10 or more points. Bigger gains (20 or 30 points) are not uncommon. But if you're saying "I'm a bad test taker" as an excuse for not putting in the time, then I don't have much sympathy for you. Law is hard. The LSAT is nothing compared to how hard you'll have to work in law school, and law school is nothing compared to how hard you'll have to work in practice. If you're not willing to work hard, and work on your weaknesses, then you may as well just stop now.
The only downside to removing "I'm a bad test taker" from your vocabulary is that you're going to have to face the real reasons why you're not doing as well as you'd like on the LSAT. It's a painful first step toward reaching your LSAT goals. But once you remove that barrier, the sky is the limit. I've seen tons of students walk in to my classroom with a 130-something on the first day of class, and walk out with a 160-something 12 weeks later. "I'm a bad test taker" can become "I just got a full ride to law school." I'm here to help.