Oh, if I had a nickel for every time an ISP blamed my site for their shortcomings.
They can say whatever they want. But the truth is... TestMy.net is unbiased in its results. The results you get here are a real world scenario not a best case scenario. The tests that your ISP sends you to is tested under best case scenario conditions. The funny thing is, Time Warner Cable says that this test is inaccurate... yet before they had their own test they used to send their customers here. Actually, I'm pretty sure that back in the early 2000's a tech support operator told us that TestMy.net was actually in their handbook, a part of their troubleshooting procedure.
Think about this, they have the ultimate incentive to have you test your connection with as little variables as possible. A company like TWC can save millions in service calls by making you feel all warm and fuzzy when you use their 'approved' tests and score high. "Oh, the problem must be the websites you're visiting..." --- The truth is though, if you didn't feel like their results were BS you wouldn't have come looking for this site. Right? You can feel that your connection isn't right... correct?
Speedtest.net self admittedly alters your results. They DROP the bottom 30% and top 10% of the results... to make up for the fact that flash isn't a good protocol to use for testing Internet speed. They also open 4+ threads... meaning that you're doing multiple downloads at once. Sorry, but a good connection with a quality route can max out with only one thread. It makes connections look better than they are.
I can't see Time Warner's speed test (apparently it's only available to Time Warner customers... they must not want their test under third party scrutiny.).
...If their test is made by Ookla... the same is true because Ookla is the creators of speedtest.net.
The results here have been trusted by MANY people for MANY years before Time Warner even thought of hosting their own test. Far longer than speedtest.net has been around. Choose to believe what you want to believe but realize... this isn't my first rodeo. Testing connection speed is all I do and I have no vested interest in making your connection look better or worse than it is. TMN has multiple gigabit (1000 Mbps) uplinks into one of the most powerful networks on the planet (currently over 2000 Gbps of available bandwidth, peering with over 25 Tier 1 providers... Time Warner actually peers directly with my host with 8x 10Gbps connection), hundreds of thousands of websites are hosted on the same network. If your speed is effected to TestMy.net, it's effected elsewhere too.
... Like I've said before. Which do you think is a more accurate portrayal of your speed? Testing from next door or testing where the websites you visit are actually hosted? Testing with a test that alters the results or one that doesn't?
Having said that, your speeds aren't all that bad. Now, when you paid for 20 Mbps and got 10, different story. It would be better to see 80%+ of what they quote, which would be 40 Mbps