GRE® tests all provide the ScoreSelect® option, which means you can take a GRE test once now, or again in the future, and only send the GRE test scores from whichever test date(s) you want schools to see. Best of all, you always have five years to decide. Here's how it works:
On test day, when viewing your scores at the test center*, you can choose not to send your scores at this time OR you can select either option below for each of your four FREE score reports:
Most Recent option — Send your scores from your current test administration.
All option — Send your scores from all General Test administrations in the last five years.
After test day, you can send additional score reports for a fee and select from these options for each report you'd like to send:
Most Recent option — Send your scores from your most recent test administration.
All option — Send your scores from all test administrations in the last five years.
Any option — Send your scores from one OR as many test administrations as you like from the last five years.
No matter which option you choose:
You will select by specific test dates, so your scores are all from the same testing session. The schools you designate will only see the scores that you selected to send them. There will be no special indication if you have taken additional GRE tests.
ETS全球官网(招生官的常见问题及ETS回复):
If a test taker took the GRE or TOEFL test more than once, can I see all of those scores?
GRE test takers can choose which scores to send to designated institutions with the ScoreSelect option. Institutions will only see the scores that test takers designate them to see.
TOEFL test takers can also choose which scores to send to institutions.
ETS美国总部解释:
Until the introduction of Score Select in 2014, the GRE policy did require all valid GRE scores be sent to the DI.
So it is likely the institution, that has the statement you cited on their website, is not aware of Score Select and the fact that they have no way to see any scores now unless the test takers send their scores directly to the institution. The statement is now outdated and inaccurate.
The admissions committees has no access to the GRE database and cannot extract scores at will.