So MAP is adaptive, which does mean that if one answers more questions correctly, the next questions will be harder, but there is still a ceiling on the difficulty level of questions, because there are three different levels of test, none of which contain the entire spectrum from easiest to most difficult.
It is not uncommon for teachers and administrators to have an incomplete grasp of the meaning of MAP scores. This is a separate question from a grade skip into fourth grade. I would consider the content of third grade, as well as her MAP scores. For instance, in reading, third grade is still predominantly about mastering decoding skills and approaching reading fluency. Comprehension is just beginning to enter the curriculum standards. It seems likely that she has already mastered those skills. Writing, on the other hand, is a different matter, which is not assessed on MAP anyway. One hopes that school personnel recommending a grade skip have already taken that into consideration, with first-hand knowledge of her current writing skills, and of the expectations for a beginning fourth-grader. In math, there are essentially no new concepts introduced in third grade. Multiplication is usually introduced as a concept in the end of second grade, with the bulk of third grade spent acquiring mastery of multiplication facts, fluency with addition and subtraction facts, and application of addition and subtraction to up to 3- or 4-digit numbers. There are also a few stray side skills in there, such as time and money, very light data analysis (some graphs and charts), and a little bit of fractions, usually with common denominators. If you have concerns, take a look at your state or province's curriculum frameworks. Or you can ask your school to give her the end-of-grade test (or, more likely, a series of end-of-unit tests) out of the third-grade math book. But honestly, this is not one of the grade levels that I would worry about skipping. Not a lot of new concepts are presented between grade one and six, outside of the four basic operations, fractions, and decimals.
Personal anecdote: I skipped half of third grade (transferred from third to fourth mid-year), and one of our children skipped all of fourth, without having been placed in SSA or any other above-grade-level instruction prior to the skip. No gaps noted in either case.
I would say, yes, she does appear to pick up math skills quickly and easily, so acceleration should be a serious consideration.
