Does having received a draft notice make someone a veteran?

Last night a person that I know from a local motorcycle group (not Legion) said that the group honored her father who recently passed with a flag line. She said that they pressured her into the flag line even though her father never served in the military and she told them that. The headquarters President justified it by saying, “Well he received a draft notice, didn’t he?”

Later in the conversation, she mentioned one of our mutual friends as being a veteran and that he would not have allowed anything like stolen valor. I told her he was not a veteran and that we actually both belonged to the same American Legion and he grew up hanging around the American Legion post, but he is a member of the Sons of the American Legion; he is not a Legionnaire, not a dual member, and he is not a veteran. We argued for about five minutes over this and I finally hung up.

I’m returning my colors tomorrow; I never even wore them but I don’t feel comfortable with this group now.

I see the draft notice as different from actually having served. Am I wrong?

03/16/2020 Edit: Yesterday, one of the members contacted me back and clarified, "The flag lines are for anyone we want to honor, first responders, military, and our families are very high on the list." As they say here in Phila, "I'm feelin some type of way about this." I told him he needs to educate the entire group on who their flag lines are for, and as a representative of the organization, the secretary should know better.

03/23/2020 Edit: The moto group is NOT the Legion Riders -just a local moto org that promotes themselves a veterans and first responders group)

09/07/20 Edit: Well, after much anxiety, I wanted to update about this. Covid hit and I haven't been back to that group. The Sgt at Arms felt I shouldn't make any hasty decisions, but I just knew it wasn't a right fit. More recently, after watching the group respond to peaceful BLM march with "No they don't" when marchers proclaimed, "Black Lives Matter," and screaming at the marchers "Black Lives Splatter," display their flag line as if fellow protesting citizens aren't patriotic, use the local VFW with confederate flags and a woman veteran screaming and flipping off protesters, and watching two of their trucks dump black diesel smoke right in front of peacefully marching protesters, I cut ties with the group by initially removing the vast majority from facebook. The very next day, their Sgt At Arms felt the need to send me a private message on FB, "I see you unfriended me, friend," with a big ole thumbs up, which I ignored. A few days later, he sent me this big long Trump rant about how he was supporting troops (he never served) and I let him have it. I told him I don't care who he votes for, but his behavior doesn't represent me, and if he contacted me again, I'd file harassment charges -and I blocked him on messenger. Two days later he sends a text, "I've been ordered to collect our patches from you. Namely our backpatch and alpha chapter." I told him I burned them and that if he contacted me again, I'd involve the police. So that's that. Always go with your gut.