DAC silently swallows tokenization errors in sp_msforeachdb

Question

This morning I hopped on the DAC to check something out. Oops, I made a typo!

1> exec sp_msforeachdb N'
2~ use [?]
3~ select N'?', count(*) from sys.sysrscols;
4~ '
5> go
1>

Can you spot my error? Pretty obvious when you see it, right? It's even more obvious if you type that command into SSMS.

Frustratingly, it took me a long time to figure it out. You will note that no error message is returned from the batch ¹ (indicated by the 1> on the newline after go)

Maybe errors get handle differently in the DAC? No... doesn't look like it...

1> select 1/0 -- simple error
2> go
Msg 8134, Level 16, State 1, Server VANDIVIER, Line 1
Divide by zero error encountered.
1> select ( -- syntax error
2> go
Msg 102, Level 15, State 1, Server VANDIVIER, Line 1
Incorrect syntax near '('.
1> exec (N'select ('); -- syntax error in deferred command
2> go
Msg 102, Level 15, State 1, Server VANDIVIER, Line 1
Incorrect syntax near '('.
1> exec sp_executesql N'select ('; -- sp_executesql
2> go
Msg 102, Level 15, State 1, Server VANDIVIER, Line 1
Incorrect syntax near '('.
1>                                                   

So clearly the DAC returns most errors to the client in just the way we expect. What the heckin' heck is happening here?!

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^{1 You will also note that even though rowcount is set to on, no rowcount was returned to the client - which should have been a clue in hindsight.}