It wasn't their job to file it with the court, it was the duty and obligation of the person who "officiated" the marriage.  Sounds like they're all being rather casual about this, considering marriage something like buying a used car.  Do you charge extra for flaky clients, or do they get discounts?

"A wedding officiant leads a marriage ceremony, verifies the information on the marriage license, and signs and completes the officiant’s section of the marriage license.

Often the most important part of the officient's job though, is registering the physical copy of the marriage license with the Clerk's Office. Until a license has been recorded, that couple has not been married under Indiana law.

While the couple has 60 days from when the marriage license was granted to get married, the signed marriage certificate does not expire and can be filed with the Clerk's Office anytime. The marriage is not recognized by the State of Indiana until the Clerk's Office records it though."

https://www.indy.gov/activity/the-marriage-license-application-process# 

Here is what IRS cousin, Social Security said about that question:

The applicable Indiana statutory provision states:

Every person who shall solemnize any marriage, by virtue of the provisions of this chapter, shall at such time give the original certificate to the persons married by him and, within thirty (30) days thereafter, file the duplicate certificate in the office of the clerk of the county in which the license was issued, which certificate shall be recorded by the clerk, together with such license ....

Ind. Code Ann. 31-1-1-5 (West 1985). The minister failed to adhere to the statutory requirement. Thus, the issue is whether the failure of the minister to file the original certificate rendered the claimant's marriage to Steven M~ void.

Indiana was an early subscriber to the view that "the presumption in favor of matrimony is one of the strongest known to the law." Teter v. Teter, 101 Ind. 129, 132 (1885). See also Rainier v. Snider, 174 Ind. App. 615, 369 N.E. 2d 666, 668 (1977). In Teter, the Court said at 101 Ind. 134:

Persons may be punished for not obtaining licenses to marry, or for not taking steps to secure a proper record of the marriage, but there may, nevertheless, be a valid marriage. The want of form, or the lack of ceremonial rites, does not impair a marriage contract, in cases where it is entered into from good motives and with an intention to contract a present marriage, and is followed by an open acknowledgment of the marital relation. (emphasis added)

By legislative enactment prohibiting common law marriages, the failure to obtain a marriage license rendered a marriage void in Indiana effective January 1, 1958. Ind. Code Ann. 31-1-1-3, 31-1-6-1 (West 1985); Williams v. Williams, 460 N.E. 2d 1226 (Ind. App. 3 Dist. 1984). Thus, the portion of the Teter opinion stating that the failure to obtain a marriage license does not impair an Indiana marriage is no longer applicable. Charles G. O~ ~, RA V (K~) to ARC Programs-Region V, 6/5/84.

However, the portion of the Teter opinion holding that the failure to secure a proper record of the marriage does not impair the marriage contract appears to remain applicable. Although we have not found any post-Teter Indiana decision addressing the issue, all cases we have found from other jurisdictions have held that the failure to record a marriage license does not effect the validity of the marriage. State v. Walker, 36 Kan. 297, 13 P. 279 (1887); Re Love, 42 Okla. 478, 142 P. 305 (1914); Kriznan v. Industrial Accident Commissioner, 14 Cal. App. 2d 419, 58 P.2d 405 (1936I; Madison v. Lewis, 151 Pa. Super. 138, 30 A.2d 357 (1943); In re Campbell's Estate, 260 WIS.625, 51 N.W.2d 709 (1952); In re Liberman's Estate, 162 N.Y.S.2d 62 (1957). The registration or recording of a marriage is not essential to its validity because such provisions are addressed to the officials issuing the license, certifying the marriage and making proper return and registration or recording, rather than to the parties to the marriage. 52 Am. Jur. 2d Marriage §41 (1970).

Accordingly, we conclude that the failure of the minister to file the duplicate marriage certificate for recording did not render claimant's October 29, 1983 marriage void.

https://secure.ssa.gov/POMS.nsf/lnx/1505405017