Yes, some states have laws (not to be confused with regulations which can be waived by the boards) that say that the exam must be passed after the requisite experience. Unless a provision is written in law for the board to waive the requirement, the board is bound to obey those laws.
For example in Pennsylvania, which has one of the most restrictive start dates for experience:
for reference:
[ (a) and (b) removed for simplicity, emphasis mine]
and in case you were wondering about out of state EITs:
So Pennsylvania by law, has to check that the applicant applying for license by comity, had met the progressive experience requirement of four years after issuance of EIT and the date of the PPE exam, to grant licensure.
And applicants can't apply until they have the four years under their belt. So a typical springtime graduate who gets in their paperwork ASAP won't get their EIT until June, which is also when the deadline for applying for the Oct exam. So nearly everyone has to wait 4 years and a few months to take the April exam instead. Someone who has a once/yr October exam effectively has a five year experience requirement before sitting for the exam. Of course the CBT is making this go away, but it still sucks.
And BTW, PA has actually relaxed its requirements in the last 20 years! When I was an undergrad, the experience had to be gained under a licensed PE in the same discipline as the applicants undergraduate degree! It was making it nearly impossible to license engineers in the Commonwealth in certain disciplines. And the graduate degrees had to be in the same discipline as the undergrad or they wouldn't count as experience either. Thankfully they changed those rules earlier this decade.
There are many other states with similar laws or restrictive regulations. I am listing Pennsylvania because its one of the two jurisdictions with which I intimately familiar with the laws and regulations.
tl;dr YES, always look at the other states requirements