SACSegmentation detecting odd plane model

I'm trying to fit a plane model to a point cloud (with a plane-like structure).

The problem I'm encountering is that the fitted plane is just a small slice of the cloud, even if the distance threshold is set to a relatively large value.

Here are some images of the result: (white points are model inliers)

You can see how thin the cloud is here:

I've tweaked all sorts of parameters for the SACSegmentation object and even tried multiple RANSAC methods that PCL has with no luck.

This is the point cloud displayed: https://drive.google.com/file/d/0B0PUIShwQuU7RmFKUW1Cd2V1Zk0/view?usp=sharing

Here is the minimal code that follows the tutorial pretty closely:

#include <iostream>
#include <pcl/ModelCoefficients.h>
#include <pcl/io/pcd_io.h>
#include <pcl/point_types.h>
#include <pcl/sample_consensus/method_types.h>
#include <pcl/sample_consensus/model_types.h>
#include <pcl/segmentation/sac_segmentation.h>


int
main(int argc, char** argv)
{
    pcl::PointCloud<pcl::PointXYZI>::Ptr cloud(new pcl::PointCloud<pcl::PointXYZI>);
    pcl::io::loadPCDFile<pcl::PointXYZI>("test.pcd", *cloud); //* load the file

    pcl::ModelCoefficients::Ptr coefficients(new pcl::ModelCoefficients);
    pcl::PointIndices::Ptr inliers(new pcl::PointIndices);
    // Create the segmentation object
    pcl::SACSegmentation<pcl::PointXYZI> seg;
    // Optional
    seg.setOptimizeCoefficients(true);
    // Mandatory
    seg.setModelType(pcl::SACMODEL_PLANE);
    seg.setMethodType(pcl::SAC_RANSAC);
    seg.setDistanceThreshold(0.025);

    seg.setInputCloud(cloud);
    seg.segment(*inliers, *coefficients);

    if (inliers->indices.size() == 0)
    {
        PCL_ERROR("Could not estimate a planar model for the given dataset.");
        return (-1);
    }

    std::cerr << "Model coefficients: " << coefficients->values[0] << " "
        << coefficients->values[1] << " "
        << coefficients->values[2] << " "
        << coefficients->values[3] << std::endl;

    //add points to plane that fit plane model
    pcl::PointCloud<pcl::PointXYZI>::Ptr output(new pcl::PointCloud<pcl::PointXYZI>);
    for (size_t i = 0; i < inliers->indices.size(); ++i)
    {
        output->push_back(cloud->points[inliers->indices[i]]);
    }

    displaySubcloud(cloud, output);
    displayPlane(cloud, coefficients, "plane");

    return (0);
}

I've figured out a solution, but I don't know why it fixes it. By translating the cloud closer to the origin, it is able to detect the correct plane model.