The Opinion Rule
What you refer to as ipse dixit is dealt with by the opinion rule. In summary, witnesses are required to testify to facts, not opinions - it is for the judge/jury to reason from facts to conclusions.
In New South Wales, this is stated in s76 of the Evidence Act 1995 which codified the common law rule applicable in most common law jurisdictions.
76 THE OPINION RULE
(1) Evidence of an opinion is not admissible to prove the existence of a fact about the existence of which the opinion was expressed.
Which is a little bit opaque to the non-legally trained so the act helpfully gives some examples:
1 P sues D, her doctor, for the negligent performance of a surgical operation. Unless an exception to the opinion rule applies, P's neighbour, W, who had the same operation, cannot give evidence of his opinion that D had not performed the operation as well as his own.
2 P considers that electrical work that D, an electrician, has done for her is unsatisfactory. Unless an exception to the opinion rule applies, P cannot give evidence of her opinion that D does not have the necessary skills to do electrical work.
There are a number of exceptions to the opinion rule; the relevant one for your question is the expert opinion exception. s79 deals with this:
79 EXCEPTION: OPINIONS BASED ON SPECIALISED KNOWLEDGE
(1) If a person has specialised knowledge based on the person's training, study or experience, the opinion rule does not apply to evidence of an opinion of that person that is wholly or substantially based on that knowledge.
If the court (and subsequent appeals courts) accept that a witness is an expert and the opinion is limited to the field of their expertise and the opinion is representative within the context of that expert community (i.e. the expert is not an iconoclast or is using unacceptable techniques), they are entitled to express it. Indeed, that's why courts use expert witnesses.