I agree with this, but I would add a few things.
In my honest opinion, based on what I have seen recently, England's pitches aren't massively favourable to them and haven't been for a while. I have read a lot of comments where some India fans are convinced that every English surface is a 'green top', but even if this were true, the greenness wears off by day 2. Overhead conditions can also be pretty unpredictable but are in no way 'planned' by the home side.
The Oval, Lords, and Old Trafford are usually on the roster of pitches selected for the main tour and they tend to favour spin and fast bowling, where England have historically lacked options. England's record at these grounds in recent times is pretty ordinary because they have not had a front line spinner since Graeme Swann, who was probably a 'once in a generation' type player for us. If you get The Oval at the end of a dry English summer, then your spinners will be in the game while England will be turning to Jack Leach or Dom Bess. Same with Old Trafford and even Lords nowadays. Generally speaking, summers in England are getting hotter and it's no coincidence that England tend to fare worse when tests are played down south. Contrast that to the seventies when temperatures were a lot cooler and a game was even snowed off in June 1975 between Derbyshire and Lancashire. To suggest that the deck is stacked against India in England requires a degree of exaggeration.
Edgbaston, Trent Bridge, and Headingley tend to harness more 'English' conditions that favour swing and seam. It's worth noting that England could include other clearly trickier grounds like Chester-le-Street and Hove if they wanted to exagerrate their advantage, but an India/Pakistan series is not so much about England trouncing the opposition as creating an even contest that people are going to watch at the ground or at home.
On the other hand, in India, if a pitch turns big from ball one, batting is just going to get progressively harder. The spectacle just becomes monotonous and predictable fare, so I don't think this is a clear case of 'six of one...'