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Reproducible Example

import pandas as pd

df = pd.DataFrame(
    {"foo": list(range(0, 5)), "bar": list(range(1, 6)), "baz": list(range(2, 7))},
)
print(df.rolling(window=3, on='foo').max())

#   bar  baz
#0  NaN  NaN
#1  NaN  NaN
#2  3.0  4.0
#3  4.0  5.0
#4  5.0  6.0

df2 = pd.DataFrame(
    {"foo": list(range(0, 5)), "bar": list(range(1, 6)), "baz": list(range(2, 7))},
    index=['1', '2', '3', '4', '5'],
)
print(df2.rolling(window=3, on='foo').max())

#   foo  bar  baz
#1    0  NaN  NaN
#2    1  NaN  NaN
#3    2  3.0  4.0
#4    3  4.0  5.0
#5    4  5.0  6.0

Issue Description

According to the document,

For a DataFrame, a column label or Index level on which to calculate the rolling window, rather than the DataFrame's index. Provided integer column is ignored and excluded from result since an integer index is not used to calculate the rolling window.

The column 'foo' should be exclude from the final results. But with a string index, it still shows up in the result.

Expected Behavior

The column 'foo' should be exclude from the final results.

Installed Versions

INSTALLED VERSIONS ------------------ commit : 2e218d10984e9919f0296931d92ea851c6a6faf5 python : 3.9.16.final.0 python-bits : 64 OS : Darwin OS-release : 21.4.0 Version : Darwin Kernel Version 21.4.0: Mon Feb 21 20:35:58 PST 2022; root:xnu-8020.101.4~2/RELEASE_ARM64_T6000 machine : arm64 processor : arm byteorder : little LC_ALL : None LANG : None LOCALE : None.UTF-8 pandas : 1.5.3 numpy : 1.23.5 pytz : 2022.7 dateutil : 2.8.2 setuptools : 65.6.3 pip : 23.0.1 Cython : 0.29.33 pytest : 7.1.2 hypothesis : None sphinx : None blosc : None feather : None xlsxwriter : None lxml.etree : None html5lib : None pymysql : None psycopg2 : None jinja2 : None IPython : 8.11.0 pandas_datareader: None bs4 : None bottleneck : 1.3.5 brotli : fastparquet : None fsspec : None gcsfs : None matplotlib : None numba : None numexpr : 2.8.4 odfpy : None openpyxl : None pandas_gbq : None pyarrow : 8.0.0 pyreadstat : None pyxlsb : None s3fs : None scipy : 1.10.0 snappy : None sqlalchemy : None tables : None tabulate : None xarray : None xlrd : None xlwt : None zstandard : None tzdata : None