Recycling a tin can
We ignore that the claim has no source cited and assume it is true. I arbitrarily chose the Samsung UA32K4000ARLXL. Its maximum power usage is 72 W.[1] Accounting for older (and thus presumably less energy efficient) models we estimate the average power usage of a TV to be 100 W. Operating for 3 hours, this TV would consume 300 Wh of electricity. The total energy consumption per person in the UK is estimated to be 125 kWh per day.[2] This implies that recycling the tin can saves 0.24% of the energy we use daily. In alternative units, one needs to recycle more than 400 tin cans per day to be “energy neutral”. Cf. PET plastic water bottles, which we need to recycle 255 per day.[3] The two values having the same order of magnitude gives some credit to the original claim.
[1]: http://www.samsung.com/in/tvs/hd-k4000/ [2]: Mackay, D., Sustainable Energy - without the hot air (2008). [3]: Shercliff, H.R., Part IA Paper 2: Structures and Materials - Materials Examples Paper 4 - Strength-limited Design, Process Selection, and Environmental Impact of Materials (2014). CUED.