According to Bob Flexner, Tru-Oil is a polymerized oil, which turns it into a type of varnish, and Danish Oil is really an oil/varnish blend. They may have started as linseed oil or have been mixed with it, but they aren't the same thing.
A couple of quotes from the book, both from chapter 5:
Understanding Oil
"They (oils) also cure soft. /snip/ You can't build a thick, hard, protective film on the surface of the wood the way you can with film finishes. "
Polymerized Oil
"This (polymerization), or an equivalent process, is what is done to /snip/ Tru Oil."
This changes the oils so that they complete their curing rapidly /snip/ and it makes the oils cure hard and glossy. In contrast to normal linseed oil and tung oil, it's possible to build the oils to a thickness on the surface of the wood"
So while Tru Oil may have started as an oil, it has been chemically altered, no longer behaves as one, and for our purposes shouldn't be considered one. It should be classigied as a film finish because it can be built up, just like the "big three".
You're right that the "big three" don't give the oiled finish feel. The closest you'd be able to get is with only one or two coats of shellac that's been buffed with steel wool. It won't be as "slick" as oil, but you can still feel the wood.
My honest suggestion would be to get some Tru Oil and linseed oil and test them both to see which one you like better. They both behave differently and will give a different result. Wez & I can peacefully debate the semantics all day long and never help you as much as that would.
I can offer first-hand testimony that Danish Oil and linseed oil feel very different, and that linseed is far superior in that realm. The end result also looks better. But that's also MY feel & taste, not yours.