Unless you are way deep into friend zone territory, a girl moving with you is a significant sign of interest, because people are unlikely to give such a significant investment to someone they don't like.
Think of compliance as a scale, where the higher up we go the more demanding the request, and the more unlikely the average person is to comply.
If I'm with a girl and I tell her to get on her knees and suck me off, and she does it, I have a very good idea of where I stand. That's a pretty damn high level of compliance and (and very satisfying when it works). I can be relatively sure that a girl who complies with that request is, in fact, very interested in me. Either that or she is being paid a significant amount of money.
That is one extreme end of the spectrum. On the other side, what if I walked up to random girls and asked them for the time? I haven't conducted a field trial on this, but I'm willing to bet my response rate would be close to 100%, and would have no correlation to the girls interest in me. Why?
Because the level of compliance and investment I am asking for is so low. Giving the time is a common favor that virtually anyone would do for anyone else.
Look at it from your perspective; if someone (could be a girl or a guy) asks you to move somewhere with them while you are out at a bar, what kind of people are you likely to say yes to? I'd venture that its high-value interesting people with a lot of social value for men, or attractive potential mating partners for women.
If Ugly Mcfatterson strolled up to you and asked you to buy her a drink you would, hopefully, say no, but if Hotty von Bigtits made the same proposition you might be otherwise inclined.
When you get a girl to physically follow you somewhere, it shows a commitment to the interaction and a level of compliance that goes beyond what would be found in a normal conversation between strangers. The more you are making a girl move the bigger the ask and the more unlikely the average girl is to say yes, thus the more accurate it will be as a screen to show their interest level.
Compare getting getting a girl to move a foot closer to you so you can hear each other, to getting a girl to move to a different room and sit down with you, to getting a girl to leave the bar with you altogether. You should be able to instinctively tell that these things are not on the same level and would take different amounts of buy-in from a girl to accomplish.
Finally, from a more advanced perspective, getting investment from a girl is one of the biggest ways to GAIN attraction, and a girl giving you compliance is also giving you investment.
Does that answer your question?