Why indeed? Spanish-American War veterans would have applied to the Federal government for pension support, but only after Congress made provision for it. Don't know when or how that was.
I'd guess that Parnell might have told family and friends that he served in both wars. It didn't cost much to apply, and even if the widow submitted very little information, the pension board may have been inclined to grant it. By the 1920's most veterans and their widows had gone on to their reward, and the state pension fund may have been flush with cash.
You would do well to obtain copies of these documents.