Yes. Collins brings out these differences:
simply [adverb] [adverb before verb {phrase}, adverb adjective]
You use simply to emphasize what you are saying. [emphasis]
- This sort of increase simply cannot be justified.
- So many of these questions simply don't have answers.
- In a poll of those leaving the theatre and nine out of ten thought it was simply marvellous.
This 'simply' is a pragmatic marker, relating to the whole statement:
'Let me put it simply: one does not walk into Mordor.' or
'One does not walk into Mordor. It's as simple as that.'
......
The second positioning rather uses the senses (and I'd say fused):
simply [adverb]
(1) in a simple [uncomplicated, undemanding] way
(2) merely, only
[just]
This 'simply' addresses the walking into Mordor:
'You can't just walk into Mordor as if you're out for an afternoon stroll.'
This is more the traditional adverb role, and note that the adverb is closer to the verb 'walk'.
I agree, the first statement offers less hope.