Seems like there's not enough room, not sure what else to say.

What brand rails do you have?

Right now all I have to test fit on is my PRI tube. So high quality rails. Thanks, should have included that initially.

There are a few rail accessories that seem to fit a little tight against 1913 rails. Amongst these are some of the TD grips and some of the FOBUS/First Samco light mounts. This has been covered in previous threads. You are not the first to experience it.

Tapping with a rubber mallet sometimes does the trick to get your accessory into place, while others require some light sanding. You could always try sending it back with a description of your problem. Myself, I usually just "make it work", but that doesn't appeal to some folks. Might try doing a search to see what others have done.

ETA: both accessories I described were composite material and not an alloy. If you can get it on and off a few times, the rails themselves usually shave off a little bit of the plastic/fiberglass/etc. material so it will move freely. Didn't damage any of the things I have ever done this with.

We know for a fact that TD conforms to 1913 Mil-Specs because a schematic is included with each TDVG.

Whether or not your PRI rail does, I don't know.

For example, my TDVG didn't fit my YHM Non-FF HG's. The TDVG required Dremel work to interface properly. As discovered, YHM wasn't up to the Mil-Spec standard and eventually corrected the error.

The TDVG fits tight on just about every other Rail system out there that strictly adheres to the 1913 specs. It should require effort to mount because you want it to fit tightly.

HS1

Mine went on with a little difficulty using the YHM 2-piece 4-rail handguards.  Once it was on... ROCK SOLID.

Just continue to work it back and forth, use tooth pics to hold the locks open.  I pounded my handguards against the carpeted floor while grabbing the VFG (kinda of like a hammer), worked for me.

I had to beat my TD vertical grip onto my YHM two-piece handguards.  Took a lot of work, but it is on there SOLID.  The rubber mallet idea is a good one.

beat it like a step child!

Quoted: beat it like a step child!

Like a rented mule.....

Quoted: Quoted: beat it like a step child! Like a rented mule.....

Like it owed you money...

Quoted: We know for a fact that TD conforms to 1913 Mil-Specs because a schematic is included with each TDVG. Whether or not your PRI rail does, I don't know. For example, my TDVG didn't fit my YHM Non-FF HG's. The TDVG required Dremel work to interface properly. As discovered, YHM wasn't up to the Mil-Spec standard and eventually corrected the error. The TDVG fits tight on just about every other Rail system out there that strictly adheres to the 1913 specs. It should require effort to mount because you want it to fit tightly. HS1

It didn't fit my KAC M4 RAS's, either. So, I tried two other sets. The other two were both issue units, the first was a unit I bought off the EE (these things are identical, but listing where they came from anyhow). Same result everytime. Required some tapping.

As far as "should require effort", IMHO that is debatable. I've yet to come across a KAC VFG (or any other VFG, save a few TD VFGs and a couple cheap knock off's) that wouldn't slide right on.
So, to say "We know for a fact that TD conforms to 1913 Mil-Specs" because there is a schematic doesn't prove much. If that is the case, then 3 KAC RASs (again, 2 of these were contract issue) were out-of-spec. But, I am highly doubting that. I even tried a friends new TD VFG. It wasn't quite as tight - I could get it on without as much tapping; but tight nonetheless.

The TD VFG may be designed into 1913 specs, but there must be some slight variances in some of the production items.

I put a TD vertical grip on my YHM free float handguards and it is tight.  I actually pushed so hard it went all the way down to the end of the rail right up against the mag.  I had to use a rubber mallet to tap it into place but now it is nice and solid.