The first thing, she should be able to use ISO 6400 with 70D. I manage it with my older 7Ds (though I try to keep them to 3200 or 1600 or below, as much as possible, since it will mean less work later). I almost never use my 7Ds lower than ISO 200 or 400.... they produce their cleanest images between at 400 and 800 (Canon appears to turn off automatic in-camera noise reduction at the lowest ISOs). I also use slightly higher ISOs to keep my shutter speeds a little faster... I found the 18MP and higher resolution crop sensor cameras seem a little more susceptible to camera shake blur than earlier, lower resolution models I used (Some years ago Canon issued a white paper about this, too, recommending higher shutter speeds for this reason.)
The keys to using high ISO w/Canon are...
Shoot RAW and avoid underexposure like the plague. Then post-process the images with some careful noise reduction applied. (I do batch RAW conversions with some extra NR dialed in with Lightroom to make smaller proofs... but then use Photoshop with a Noiseware plug-in to make finished images from high ISO shots. There are other s'ware combinations possible... this is just what works well for me.)
What I mean by avoiding underexposure is you never want to have to increase exposure or "brighten" high ISO images in post-processing. That greatly amplifies noise. In fact, it's much better to err toward slight (+1/3 or +2/3 stop) overexposure, then reduce exposure or "darken" your high ISO shots in post. That will help minimize the appearance of noise. Also, don't do any final sharpening until after the noise reduction and sizing/cropping is complete... and be careful not to over-sharpen. Sharpening can increase the appearance of noise too, so it's important to deal with the noise first.
Beyond that... a lot of time concerns about image noise are vastly overblown by pixel peeping. Hell yes, if you look at the image a 100% you'll see noise. But that's equivalent to making a five foot wide print from a 70D image file, then viewing it from 18" away. If you are making an 8x12 or even a 13x19 print from that image, you won't see the noise unless you're using a magnifying glass! You certainly won't see it at Internet resolution and sizes. Back off to 25% or 33% when evaluating image noise (and focus, and sharpness). That's still pretty large, but much more realistic size for most of our actual uses! (Zoom in freely to do retouching, of course.... Just not for evaluation purposes.)
This was shot with 7D at ISO 3200 (some post-processing adding background blur mostly... has been printed 11x14" )...
This with 7D at ISO 3200 (little post-processing, has been printed 16x24" )...
This with 7D at ISO 1600 (minimal post-processing... mostly to increase contrast due to dust!)...
This with 7D at ISO 800 (no special post-processing)...
Granted, none of the above are "night shots". Two are outdoors in shade and/or with overcast... and two are in covered (dark!) arena's with strong back-lighting. But if sports are taking place indoors or at night, there has to be some sort of lighting that's at least equal to that of a covered equestrian arena.
Next, fast lenses... f2.8 or better... can help. Here we're talking money, in most instances. But some primes such as 85/1.8, 100/2 aren't too expensive. The trade-off is depth of field... it can be too shallow with larger apertures...
Depending upon focal length and working distances, as well as the aperture being used, DOF can be extremely shallow. This was shot with 135mm lens at f2.0 on Canon 5D Mark II (at ISO 6400)...
The other difficulty is going to be achieving focus in low light conditions. Here my older 7Ds will probably do better, since the 70D's similar AF system is a slightly downgraded version of the 19-point AF. The 7D has a separate chip running the AF (much like the 1D series cameras), which the 70D does not. Even so, it can be a struggle. USM lenses help. As do larger apertures, once again. But, once again, we're talking money.
One way to deal with slow or hunting AF issues is to pre-focus on a particular spot where you know the subject eventually will be, then lock the focus and wait for the subject to come there, tripping the shutter at just the right moment.
The only other alternative is a different camera. 5D Mark III is able to focus about 1 or 2EV lower light than her 70D or my 7D... and the full frame camera also can shoot more noise free images at higher ISOs. There's "no free lunch" though.... Full frame also will require longer lenses for sports, in particular. Rather than a handholdable 300/4, for example, a much bigger, heavier and much more expensive 500/4 - and a tripod to sit it on - would be needed to be able to frame the subject in the same way.
Note: although full frame to deliver low noise images at high ISOs and able to focus in lower light too, the 6D's simpler AF system is just not up to sports photography. Nor are the earlier 5DII's or original 5D's.
Arguably, the best cameras for sports (day or night) are the full frame 1DX and earlier, APS-H format 1DIII or IDIIN. All those are quite pricey and will still require full frame capable lenses, though. The full frame 1Ds III is also capable of focusing, but it's only able to shoot at about 5 frames per second and it's highest settable ISO is 3200, and that's an "expanded" one, from it's standard range that tops out at 1600. (Oddly, the 5D II that came out one year later using essentially the same 21MP sensor, but with ISO 6400 as the top of it's normal range, expandable to H1 12800 and H2 25,600. I always thought it a bit strange that Canon never changed their top-of-the-line FF model to be able to shoot the higher ISOs, too.)
You mention she was using Sports mode.... which is one of Canon's "Scene" presets that dictates not only how exposure is done, but also the autofocus setup and even what type file is saved (JPEG only). She won't be able to capture RAW files in that mode. I never use those highly automated modes. They don't let me set up the camera correctly... or the way I want it. I mostly use Av (Aperture priority mode) for auto exposure and keep an eye on my shutter speeds.... Less often I'll use Tv (Shutter priority) or P (Program AE). Or, I prefer whenever I can to fully lock in exposure in M ( Manual mode). I never use Auto ISO. That just confuses thing more.