I've met a lady who worked with him in Scotland, she was scathing of the LTA (with good reason, they really are piss-poor) and fully supported him moving to Spain when he was younger. She thought that Murray's family paid for him to go, I was under the impression the LTA subsidised it to some extent.
They've certainly spent a fair bit on him, and I think that much resentment is due to the LTA and others seeing him as an ingrate. He is cocky and his mother is quite vocal on his behalf, which causes additional tension. He rarely acknowledges the LTA or supports their activities - as fgar as I gather, because he doesn't think they helped him that much - even though they have invested a lot in him. He's slowly unwinding his engagement with them as well, hiring his own coaches etc. I can't really fault it, he's taking responsibility for his own career, but I think he could be a litlte bit more supportive of those who helped him early on.
I can see both why he did what he did, and she (his mother) does what she does, but also why the LTA (and, by extension, many of those involved in tennis in the UK) might be a touch aggrieved.