They are not correct. They _can_ port the number away, but it _will_ involve terminating your DSL service, on that line if they do so.
The underlying situation is the 'reservation' of the line pair for your use is allocated for the voice service, and the 'shared' DSL just 'piggybacks' on that.
Disconnecting the primary service -- as when the voice number is 'ported away' to a different carrier -- automatically terminates _all_ other 'piggybacked' services on that pair, and the pair is returned to the 'free pool' for assignment to another user, if needed. That's the 'why' behind things -- when the voice number goes away, the _physical_line_pair_ is marked as 'available for re-use'.
Note: they wouldn't _have_ to do things that way -- a significantly 'smarter' system could count services assigned to the pair, and release the line pair 'only' when the 'use count' went to zero. This would require a counter in the database, rather than just a one-bit flag, and it buys little benefit to the phone company -- although it makes life a bunch easier for customers that are 'defecting' _away_ from the current telco.
With the -current- configuration, that is all correct.
There are "real" technical issues that prevent it from happening, and the current telco has no incentive to go to the work/effort necessary to make it _easier_ for customers to leave for the competition.
1) Tell the ILEC to disconnect your DSL.
2) Place the order with Vonage, they then port the number.
3) Now, order 'stand alone' DSL from the provider of your choice.
Porting the phone number_does_ involve a disconnect of the current phone service, and the freeing up of the pair that it is currently assigned to. This automatically terminates any other service (like DSL) running on the same wire pair.
The telco, to preserve _your_ interests in the 'other services' they provide over the same pair, refuses to disconnect that main service while the piggybacked services are active.
Imagine what you would have been saying to the telco if they _had_ simply terminated the DSL -- *WITHOUT*WARNING* to you -- as part of disconnecting the line and transferring the number to Vonage.
You have to 'unwind' things back to simple phone service -only- on the line to port the number without affecting other stuff.
Converting the existing line to stand-alone DSL is accomplished by disconnecting the voice service, and, as pointed out, _then_ you don't "own" the number any longer, and cannot port it.
The "bottom line" is that they _have_ to do it, but t hey don't have to 'make it easy' for you, *and* the 'club' of the "related services" being adversely affected _is_ one that they will use in efforts to make changing away from them "less desirable".
One thing you can do, to make the telco's life "difficult" is to order _new_, additional, 'stand alone' DSL service, _before_ doing anything with the existing 'shared' DSL. that way you're not "off line" for the period that it take to do the stand-alone DSL install.
This forces them to find a second pair that can be used to reach your place. *AND* gives you some time to verify line 'quality' before going to a mode of 'depending' on it.
You will, obviously, incur double charges for the period that both DSL circuits are active, *and* (in either scenario) you'll have to start a new contract, with the new time commitment lock-in, early-cancellation penalties, etc.
***** Moderator's Note *****
If you decide to install a second DSL line prior to disconnecting Verizon, I recommend you try Speakeasy. Although they cost more than Verizon, it's worth it: they have a "bits are bits" policy, cluefull tech support that speaks American English, no port blocking, and they'll even bill your neighbor if you share a WiFi connection.
Tell them I sent you: I get a credit on my bill if you sign up! My speakeasy ID is ehorne at speakeasy dot net.