Did the Sheldrake manager think that Baby was Penny?

An anonymous commenter posted in the wrong place -- under Miscellaneous Videos - 117 -- the following comment, which obviously was intended for my post Why did Baby help Penny -- Part 3.

I'm refering to this:

"Baby's fourth step helped not only Penny, but also Johnny. Apparently, only he had signed the contract with the Sheldrake. He was the one person who was obligated by the contract to show up, with a female partner. If he showed up with a partner other than Penny, then he still fulfilled the contract."

I always assumed that Baby disguised herself as Penny. She took Penny's dress and pinned up her hair. I don't know who owned the Sheldrake (Max Kellerman? Because Neil mentions that he owns two hotels), but obviously nobody noticed the disguise.

Why should Baby be afraid that the Schumachers recognize her if it didn't matter who Johnny's dance partner was?

This comment gives me some new insights.

I always had assumed that the Sheldrake manager must have recognized that Johnny brought a new partner -- not his usual partner Penny -- to the performance that we see in the movie. How might the Sheldrake manager have been fooled?

At Kellerman's, Penny did a side job of demonstrating wigs to the female guests.

Baby and Lisa trying on wigs

Lisa managing the wigs

Although Johnny could not disguise himself effectively at the Sheldrake performances, Penny could have done so by using wigs and cosmetics. Furthermore, Penny might even have pretended to be various female partners for Johnny's performances at the Sheldrake.

I speculate further that Johnny's contract at Kellerman's permitted him to perform elsewhere occasionally, whereas Penny's contract did not permit her to do so.

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Why were Johnny and Baby concerned that Schumachers saw them performing at the Sheldrake? That concern always has puzzled me, but I have not addressed it on this blog until now.

I thought that Baby was concerned that the Schumachers might mention Baby's presence at the Sheldrake to her parents.

However, the above comment raises another possibility -- that the Schumachers might mention Johnny's presence at the Sheldrake to the Kellermans.

Perhaps Johnny and Baby were concerned about both possibilities.

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The Schumachers surely recognized Johnny at the Sheldrake, but they might not have recognized Baby in her wig and cosmetics.