Longest Common Subsequence Via Dynamic Programming

I read the wikipedia page on the Longest Common Subsequence problem to understand the LCS Table approach, but it seems to result in different solutions given different orders of the original sequences. For example, the traceback table generated here is correct, since the longest common subsequence of AGCAT and GAC has a length of 2:

   |A  G  C  A  T
---+-------------
G|0  1  1  1  1
A|1  1  1  2  2
C|1  1  2  2  2


From what I understand of how it's supposed to work, the length of the LCS should appear in the bottom right cell.

But using the same method for generating the table, which you can find here, if you rearrange the letters you get an incorrect solution.

   |A  A  G  C  T
---+-------------
C|0  0  0  1  1
G|0  0  1  1  1
A|1  1  1  1  1


Length of the LCS shouldn't have changed, the bottom right value is no longer 2.

Is my question clear enough? Am I simply following the method incorrectly? From what I understand, the order of the original sequences shouldn't matter.

By example, some subsequences of AAGCT are: AG, AT, ACT, AGT