Forget Santo Domingo: in 1867 Minister Thomas Stilwell entertained the notion of annexing Venezuela in order to avoid dealing with corruptions in customs. Such a proposal seems to be a) an absurd overreaction b) imperialist arrogance c) unlikely to come to pass, given Sumner's resistance to annexing Santo Domingo. But aside from c), these are really just standard characteristics of US policy towards Latin America. So let's remove the convenient change of behavior on Venezuela's part and the obstacle c) imposes as well: either Grant uses the old annex-by-joint-session trick, or Sumner hits his head. What would be the ramifications of the US annexing Venezuela around the late 1860s or early 1870s?
Beneath the United States: A History of U.S. Policy Towards Latin America said:No one wanted to rely upon Venezuelan officials, wrote one U.S. minister in 1867, three weeks after his arrival in the country. "Its President, its Cabinet, and Chief Officers, if one half of what I hear may be relied upon, worse than robbers, appropriating the revenues of the Government to their own use without authority of law, in fact without any, save that which might, and a rabble soldierly give them." The preceding U.S. minister had reported a few months earlier that Venezuelan judges were "subject to the suspicion of bribery and often easily controlled in their action by dislike to foreigners," and that "the honesty of almost every public man in this country is doubted."
To avoid the need to rely upon corrupt Venezuelans, Minister Thomas Stilwell proposed annexation to the United States. At this moment President Grant was having difficulty convincing Congress to annex the Dominican Republic, and so he decided that a better approach would be not simply to impose a lien but also to take actual control of Venezuela's customs collections. His proposal to this effect became moot before the new U.S. minister could deliver it, however, because Venezuela began to pay its creditors.' For a few years the government in Caracas was able to service just enough of its debt to forestall intervention, but never enough to provide full satisfaction.
Lars Schoultz. Beneath the United States: A History of U.S. Policy toward Latin America (Kindle Locations 2473-2481). Kindle Edition.