Do I need to send form 1040 with form 1040x, since 1040 changed in my amended return packet from Turbotax?

Yes. Behind the 1040X, include any tax forms that are changed due to the amendment. The 1040(A)(EZ) form itself is required in nearly all cases, but you may have other forms as well.

You only sign the 1040X, however.

I contacted Turbotax and the representative said that definitely 1040 (A)(EZ) need not be included. When I pointed out that there is an answer to this to the contrary (as above), she still stood by the fact that modified 1040 need NOT be included.

No. Tax forms that have changed do not include original Federal filing forms (1040, 1065 etc). Just the 1040x and any forms that support the changes.