You should be as cooperative as possible, but don't touch his set , and don't say that you are going to fix it. It is almost certainly not your problem, and volunteering to do anything makes you look responsible. If you touch his set, you will own it and everything that ever goes wrong with it forever.
The TS-120 is a bit aged, but it should still be pretty clean in terms of VHF harmonics. If 10 meter SSB is bothering him, you might try a low pass filter on the rig, but with modern solid state radios, that shouldn't be needed. Still, it will help to ensure that you are not radiating anything that might be bothering him.
Still, if he's getting bad interference when you aren't there, it's time to call the cable company, and it would probably help for you to be there when they come. At least it will prevent their 'expert' technician from automatically blaming everything on you if you're standing there - and don't think for one second that they won't play that card, either. Their technician may or may not have the equipment or skill to isolate and eliminate the problem, but if it's tearing up his TV and NOT tearing up your ham receiver, it's something in THEIR system, not yours.
You don't bother any of your own home electronics do you? That's usually the very first test. If you're clean on your own set/stereo/speakers/telephone, it's hard for them to claim it's your fault.
This is perhaps the BEST "pep-talk" I've ever had in my almost 26 years of being a ham. As a PBX Technician, I can tell you that I have run into those situations professionally. A customer sees me on-premises...and if the copy machine, fax machine, coffee machine happens to break within a day or two of me being there, it MUST CERTAINLY be because of something I did. I see a parallel in your logic...so I indeed will NOT be touching anything on his set.
Today, since it's sunny and beautiful (and WARM) in Elma (south of Buffalo NY), I trimmed my PAR/LNR EF-10/20/40 for SWR. So...the antenna is trimmed to "resonance" (using my Anritsu SiteMaster...a $9000 MARVEL that covers 2-4000 MHz), I have the power turned back to about 5-10 watts on the TS-120, and the ground is OK.
Finally...my apartment is a studio/efficiency. My TV, stereo, etc, is within 6 feet of my Kenwood....and even with the loop and the power turned ALL the way up, I never interfered with any of my stuff.
Thanks for the help!!!