Windows 7 Update troubles

While working on someone else's computer I noticed that svchost.exe -k netsvcs was completely hogging one CPU. Another symptom was that Windows Update was stuck at Checking for Updates... The first thing I tried was installing a new update client that allegedly fixes the problem, KB3050265. However the situation remained unchanged. I then learned about %WINDOR%\WindowsUpdate.log which contained the lines

2015-12-11 10:58:15:789 4440 3bc Handler   : Updates to install = 1
2015-12-11 10:58:46:178  964 944 Handler FATAL: UH: 0x80070490: EvaluateApplicability failed in CCbs::EvaluateApplicability
2015-12-11 10:58:46:880  964 944 Agent WARNING: Failed to evaluate Installed rule, updateId = {F9164872-3E27-4410-B4FC-038814549BB1}.105, hr = 80070490
2015-12-11 10:59:09:157  964 944 Handler FATAL: UH: 0x80070490: EvaluateApplicability failed in CCbs::EvaluateApplicability

Unfortunately it did not mention which update was corrupted. The error message took me to the System Updatze Readiness Tool via KB947821. Unfortunately, its error report was clean.

=================================
Checking System Update Readiness.
Binary Version 6.1.7601.22471
Package Version 26.0
2015-12-11 11:00

Checking Windows Servicing Packages

Checking Package Manifests and Catalogs

Checking Package Watchlist

Checking Component Watchlist

Checking Packages

Checking Component Store

Summary:
Seconds executed: 522
 No errors detected
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