What is the test for admitting a rebuttal from a witness on cross-examination?

On appeal, defendant relies on the rule that "[b]y allowing objectionable evidence to go in without objection, the non-objecting party gains no right to the admission of related or additional otherwise inadmissible testimony. The so-called 'open the door' or 'open the gates' argument is 'a popular fallacy.' [Citations.]" (People v. Gambos (1970) 5 Cal.App.3d 187, 192; People v. Williams (1989) 213 Cal.App.3d 1186, 1189-1190, fn. 1.) Specifically, defendant asserts the prosecution's cross-examination of defendant about the prior dispute was inadmissible because it was outside the scope of the direct examination, despite his counsel's failure to object. (Evid. Code, 773, subd. (a).) Accordingly, he argues, that inadmissible testimony on cross-examination could not support the trial court's admission of rebuttal testimony. The argument fails because, even if there had been an objection on the ground the questioning went beyond-the-scope of direct examination, the trial court would have been within its discretion to find the cross-examination permissible.