Technically it was their first win in the series, it just wasn't OSU's first loss to Michigan in Lacrosse. So they may have been correct, depending on how they worded it. But if they said it the same way as you did, then it'd be wrong.
Here is the series history, not including yesterday's debacle.
MICHIGAN
Overall Series: Ohio State leads 16-3
Varsity Series: Ohio State leads 7-0
Columbus: Ohio State leads 9-1
Ann Arbor, Mich.: Ohio State leads 7-2
4/13/18 .............W .................... 8-5 ...........................H
4/15/17 .............W ................... 18-7 ........................... A
4/16/16 ............W ................... 10-7 ..........................H1
4/12/15 ............W ................... 13-8 ........................... A
4/12/14 .............W ...................15-6 ......................... H2
4/13/13 .............W ................... 17-8 ........................... A
4/14/12 .............W ...................12-9 ........................... A
4/6/88 .............W ....................11-5 ...........................H
4/22/87 ...........W .................... 11-4 ........................... A
5/2/80 .............L ......................6-7 ...........................H
4/5/78 .............W ................... 14-4 ...........................H
3/27/77 ...........W .................... 11-4 ........................... A
3/31/76 ............W .....................7-4 ...........................H
4/9/75 .............L ......................5-7 ........................... A
3/18/72 ............W ....................11-6 ...........................H
4/17/71 .............L ..................... 5-6 ........................... A
4/11/69 ............W ................... 10-7 ........................... A
4/8/67 .............W ..................20-2 ...........................H
1966 ................W ......1-0 (Forfeit) ...........................H
1 Showdown in the Shoe, Ohio Stadium (attendance 24,581);
2 Showdown in the Shoe, Ohio Stadium (attendance 17,641);
Note: Michigan became a varsity program beginning with the 2012 season